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丕賱兀乇囟 丕賱賲爻胤丨丞: 賯氐丞 禺賷丕賱賷丞 賲鬲毓丿丿丞 丕賱兀亘毓丕丿
賲賳匕 馗賴賵乇賴丕 毓丕賲 佟侉侉伽 爻丨乇鬲 乇賵丕賷丞 芦丕賱兀乇囟 丕賱賲爻胤丨丞: 賯氐丞 禺賷丕賱賷丞 賲鬲毓丿丿丞 丕賱兀亘毓丕丿禄 丕賱賯乇丕亍 賵丕賱毓賱賲丕亍 毓賱賶 丕賱爻賵丕亍 賵亘賴乇鬲賴賲 亘賲夭噩賴丕 丕賱廿亘丿丕毓賷 亘賷賳 丕賱賵丕賯毓 賵丕賱禺賷丕賱貙 賵賲毓 兀賳賴丕 鬲亘丿賵 賱賱賵賴賱丞 丕賱兀賵賱賶 兀丿丕丞 匕賰賷丞 賱鬲毓賱賷賲 賲亘丕丿卅 丕賱乇賷丕囟賷丕鬲 賵丕賱毓賱賵賲貙 廿賱丕 兀賳 丕賱賳馗乇丞 丕賱賲鬲毓賲賯丞 鬲購馗賴乇 兀賳賴丕 鬲噩乇亘丞 兀丿亘賷丞 賲賲鬲毓丞 鬲丨賮夭 丕賱毓賯賱貙 賵鬲爻禺乇 丕賱乇賵丕賷丞 毓賱賶 賱爻丕賳 亘胤賱賴丕 賲賳 丕賱賲噩鬲賲毓 丕賱賮賷賰鬲賵乇賷 丕賱匕賷 賰丕賳 賮賷 匕賱賰 丕賱賵賯鬲 賳賴亘賸丕 賱乇賷丕丨 丕賱鬲睾賷賷乇.
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毓賳 胤乇賷賯 丕賱乇丕亘胤 丕賱鬲丕賱賶 ePub, KFP, PDF 丕賱賰鬲丕亘 賷賲賰賳 鬲丨賲賷賱賴 亘賴賷卅丞
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144 pages, ebook
First published January 1, 1884
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67.6k people want to read
About the author
Edwin A. Abbott
210听books768听followersPeople best know British theologian and writer Edwin Abbott Abbott for his imaginative satirical novella
Flatland: A Romance of Many Dimensions
(1884).
This English schoolmaster authored of the mathematical satire.
He was educated at the city of London school and at college of Saint John, Cambridge, where he as fellow took the highest honors in classics, mathematics, and theology. In 1862, he took orders. After holding masterships at school of king Edward, Birmingham, and at Clifton college, he succeeded G.F. Mortimer as headmaster of the City of London School in 1865 at the early age of 26 years. He was Hulsean lecturer in 1876.
He retired in 1889, and devoted himself to literary and theological pursuits. Liberal inclinations of Abbott in theology were prominent both in his educational views and in his books. His Shakespearian Grammar (1870) is a permanent contribution to English philology. In 1885 he published a life of Francis Bacon. His theological writings include three anonymously published religious romances - Philochristus (1878), Onesimus (1882), and Sitanus (1906).
More weighty contributions are the anonymous theological discussion The Kernel and the Husk (1886), Philomythus (1891), his book The Anglican Career of Cardinal Newman (1892), and his article "The Gospels" in the ninth edition of the Encyclop忙dia Britannica, embodying a critical view which caused considerable stir in the English theological world. He also wrote St Thomas of Canterbury, his Death and Miracles (1898), Johannine Vocabulary (1905), Johannine Grammar (1906). Flatland was published in 1884.
Sources that say he is the brother of Evelyn Abbott (1843 - 1901), who was a well-known tutor of Balliol College, Oxford, and author of a scholarly history of Greece, are in error.
This English schoolmaster authored of the mathematical satire.
He was educated at the city of London school and at college of Saint John, Cambridge, where he as fellow took the highest honors in classics, mathematics, and theology. In 1862, he took orders. After holding masterships at school of king Edward, Birmingham, and at Clifton college, he succeeded G.F. Mortimer as headmaster of the City of London School in 1865 at the early age of 26 years. He was Hulsean lecturer in 1876.
He retired in 1889, and devoted himself to literary and theological pursuits. Liberal inclinations of Abbott in theology were prominent both in his educational views and in his books. His Shakespearian Grammar (1870) is a permanent contribution to English philology. In 1885 he published a life of Francis Bacon. His theological writings include three anonymously published religious romances - Philochristus (1878), Onesimus (1882), and Sitanus (1906).
More weighty contributions are the anonymous theological discussion The Kernel and the Husk (1886), Philomythus (1891), his book The Anglican Career of Cardinal Newman (1892), and his article "The Gospels" in the ninth edition of the Encyclop忙dia Britannica, embodying a critical view which caused considerable stir in the English theological world. He also wrote St Thomas of Canterbury, his Death and Miracles (1898), Johannine Vocabulary (1905), Johannine Grammar (1906). Flatland was published in 1884.
Sources that say he is the brother of Evelyn Abbott (1843 - 1901), who was a well-known tutor of Balliol College, Oxford, and author of a scholarly history of Greece, are in error.
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Displaying 1 - 30 of 6,271 reviews
March 2, 2009
When you read this book, keep two things in mind. First, it was written back in 1880, when relativity had not yet been invented, when quantum theory was not yet discovered, when only a handful of mathematicians had the courage (yet) to challenge Euclid and imagine curved space geometries and geometries with infinite dimensionality. As such, it is an absolutely brilliant work of speculative mathematics deftly hidden in a peculiar but strangely amusing social satire.
Second, its point, even about itself, is still as apropos today as it was then. We still do not really know what the true dimensionality of the Universe is. It seems somehow unlikely that it is just "four", even in terms of spacetime dimensions. String theory talks seriously about thousands of dimensions. Quantum theory implements very seriously infinite numbers of dimensions. And yet we are still stuck in our 3 space dimensions mentally, hardly able to visualize the 4 in which we live "properly" unless we study theoretical physics for a decade or three, and utterly unable to mentally imagine those four embedded in a veritable Hilbert's Grand Hotel of dimensions.
Ultimately, this is a book about keeping an open mind. A really open mind -- avoiding the trap of scientific materialism and the trap of theistic idealism and the trap of any other favorite -ism you might come up with. Our entire visible space-time continuum could be nothing more than a single thin page in an infinitely thick book of similar pages, that book one of an infinite number of similar books on an infinite shelf, that shelf but one such shelf in an infinite bookcase of shelves, that bookcase but one in an infinite library of bookcases, that library but one... but by now you get the idea.
We have a hard time opening our minds up to the enormous range of possibilities, preferring to live our lives mentally trapped in a single tiny period on just one of those pages, in pointland. We may be quite unable to actually perceive the space in which our tiny point is embedded, but our minds are capable of conceiving it, and Abbot's lovely parable is a mind-expanding work to those who choose to read it that way.
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Second, its point, even about itself, is still as apropos today as it was then. We still do not really know what the true dimensionality of the Universe is. It seems somehow unlikely that it is just "four", even in terms of spacetime dimensions. String theory talks seriously about thousands of dimensions. Quantum theory implements very seriously infinite numbers of dimensions. And yet we are still stuck in our 3 space dimensions mentally, hardly able to visualize the 4 in which we live "properly" unless we study theoretical physics for a decade or three, and utterly unable to mentally imagine those four embedded in a veritable Hilbert's Grand Hotel of dimensions.
Ultimately, this is a book about keeping an open mind. A really open mind -- avoiding the trap of scientific materialism and the trap of theistic idealism and the trap of any other favorite -ism you might come up with. Our entire visible space-time continuum could be nothing more than a single thin page in an infinitely thick book of similar pages, that book one of an infinite number of similar books on an infinite shelf, that shelf but one such shelf in an infinite bookcase of shelves, that bookcase but one in an infinite library of bookcases, that library but one... but by now you get the idea.
We have a hard time opening our minds up to the enormous range of possibilities, preferring to live our lives mentally trapped in a single tiny period on just one of those pages, in pointland. We may be quite unable to actually perceive the space in which our tiny point is embedded, but our minds are capable of conceiving it, and Abbot's lovely parable is a mind-expanding work to those who choose to read it that way.
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April 27, 2012
Take a classically styled, 19th century satire about Victorian social mores鈥ress it up in dimensional geometry involving anthropomorphized shapes (e.g., lines, squares, cubes, etc.)鈥athe it in the sweet, scented waters of social commentary鈥nd wrap it all around humble, open-minded Square as protagonist.
The result is Flatland, a unique 鈥渃lassic鈥� parked at the intersection of a number of different genres, thus pinging the radar of a wider than normal audience to appreciate (or detest) it. Since I鈥檓 recommending the book, I鈥檓 really hoping for the former, as I do not want to incur a cyber-flogging (or worse) from my fellow 鈥済oodreaders.鈥�
So...um...math.
Let鈥檚 get this out of the way right now. As I alluded to in my intro, this book contains MATH. Now I hesitate to even mention that, because of the potential angst that subject causes many of my friends. I certainly don鈥檛 want people going all
鈥nd dashing away in a panic.
Rest easy and increase your calm, the math is very minor. It鈥檚 really limited to discussions of geometric figures in the context of how many spatial dimensions they inhabit. Damn, that didn鈥檛 sound good either鈥�.just trust me, you won鈥檛 need a slide rule, an abacus or a lifeline to Stephen Hawking to read the book.
However, with that said, while the math is not tricky, some of the concepts can be a little brain twisty to try and visualize. Thus, I want to caution that when you get to the section where a three dimensional 鈥淪phere鈥� is explaining a universe containing only one dimension to our two-dimensional protagonist, you should鈥�.IMMEDIATELY鈥ISCONTINUE鈥EADING鈥ntil you have:
1. burned some incense,
2. poured a big tumbler of whiskey, and
3. eaten a few 鈥減eyote鈥� brownies, because the SHIT is about to get鈥�
PLOT SUMMARY:
Written in 1884, the story is told by 鈥淎. Square,鈥� who lives in Flatland, a world of two-dimensions, which means length and width, but no depth (just like the Kardashians). The men of Flatland are multi-sided polygons, and the more sides an individual has, the greater their social standing. On the other hand, women are all simple lines and have no voice in the governing of the society.
Yep...the Flatlanders are chauvinists.
The book begins with 鈥淎 Square鈥� describing his life as part of the 鈥減rofessional class鈥� and providing details on daily life in Flatland. This section serves as a In reality, this is a pretty good satire on Victorian London society, the social caste system and gender inequality.
Later, 鈥淎 Square鈥� dreams of a one-dimensional world called Lineland, where the inhabitants exist as simple points along a straight line, as there is no other width or depth. I seriously hope you have that tumbler of whiskey and some brownies close by because you are going to need them. What follows is a fun, but somewhat confusing discussions during which 鈥淎 Square鈥� tries to explain the two-dimensional world to the king of Lineland.
Eventually, our protagonist wakes up back in Flatland, only to find that he is now being visited by a Sphere from a three-dimensional universe鈥�飞丑颈蝉办别测鈥别测辞迟别鈥辞飞. Sphere takes our flatlander on a mind-expanding, eye opening journey to witness the wonders and mysteries of the higher and higher dimensions (3rd, 4th, 5th, etc.). Afterwards, 鈥淎 Square鈥� returns to Flatland to teach the wonders of such 鈥渆nlightened鈥� dimensions to his fellow flatlanders, the result of which is鈥�
鈥ope鈥o spoilers here!
THOUGHTS:
As I sit here, sober and 鈥渕ostly鈥� peyote free, I think I enjoyed the 鈥渋deas and concepts鈥� of the story more than the actual plot. The writing was fine, but nothing that struck me as particularly eloquent. However, I鈥檝e the concepts of the story have stayed with me and I have actually become more appreciative of the material as time has gone by.
Overall, I liked the book. I think it鈥檚 worth reading, but more for the interesting ideas and mental gymnastics that the narrative puts you through than for the simply enjoyment of the plot. Still, a worthwhile read, and since it鈥檚 actually a novella, you can get through it quickly without a large time commitment.
3.0 stars. Recommended!
The result is Flatland, a unique 鈥渃lassic鈥� parked at the intersection of a number of different genres, thus pinging the radar of a wider than normal audience to appreciate (or detest) it. Since I鈥檓 recommending the book, I鈥檓 really hoping for the former, as I do not want to incur a cyber-flogging (or worse) from my fellow 鈥済oodreaders.鈥�
So...um...math.
Let鈥檚 get this out of the way right now. As I alluded to in my intro, this book contains MATH. Now I hesitate to even mention that, because of the potential angst that subject causes many of my friends. I certainly don鈥檛 want people going all
鈥nd dashing away in a panic.
Rest easy and increase your calm, the math is very minor. It鈥檚 really limited to discussions of geometric figures in the context of how many spatial dimensions they inhabit. Damn, that didn鈥檛 sound good either鈥�.just trust me, you won鈥檛 need a slide rule, an abacus or a lifeline to Stephen Hawking to read the book.
However, with that said, while the math is not tricky, some of the concepts can be a little brain twisty to try and visualize. Thus, I want to caution that when you get to the section where a three dimensional 鈥淪phere鈥� is explaining a universe containing only one dimension to our two-dimensional protagonist, you should鈥�.IMMEDIATELY鈥ISCONTINUE鈥EADING鈥ntil you have:
1. burned some incense,
2. poured a big tumbler of whiskey, and
3. eaten a few 鈥減eyote鈥� brownies, because the SHIT is about to get鈥�
PLOT SUMMARY:
Written in 1884, the story is told by 鈥淎. Square,鈥� who lives in Flatland, a world of two-dimensions, which means length and width, but no depth (just like the Kardashians). The men of Flatland are multi-sided polygons, and the more sides an individual has, the greater their social standing. On the other hand, women are all simple lines and have no voice in the governing of the society.
Yep...the Flatlanders are chauvinists.
The book begins with 鈥淎 Square鈥� describing his life as part of the 鈥減rofessional class鈥� and providing details on daily life in Flatland. This section serves as a In reality, this is a pretty good satire on Victorian London society, the social caste system and gender inequality.
Later, 鈥淎 Square鈥� dreams of a one-dimensional world called Lineland, where the inhabitants exist as simple points along a straight line, as there is no other width or depth. I seriously hope you have that tumbler of whiskey and some brownies close by because you are going to need them. What follows is a fun, but somewhat confusing discussions during which 鈥淎 Square鈥� tries to explain the two-dimensional world to the king of Lineland.
Eventually, our protagonist wakes up back in Flatland, only to find that he is now being visited by a Sphere from a three-dimensional universe鈥�飞丑颈蝉办别测鈥别测辞迟别鈥辞飞. Sphere takes our flatlander on a mind-expanding, eye opening journey to witness the wonders and mysteries of the higher and higher dimensions (3rd, 4th, 5th, etc.). Afterwards, 鈥淎 Square鈥� returns to Flatland to teach the wonders of such 鈥渆nlightened鈥� dimensions to his fellow flatlanders, the result of which is鈥�
鈥ope鈥o spoilers here!
THOUGHTS:
As I sit here, sober and 鈥渕ostly鈥� peyote free, I think I enjoyed the 鈥渋deas and concepts鈥� of the story more than the actual plot. The writing was fine, but nothing that struck me as particularly eloquent. However, I鈥檝e the concepts of the story have stayed with me and I have actually become more appreciative of the material as time has gone by.
Overall, I liked the book. I think it鈥檚 worth reading, but more for the interesting ideas and mental gymnastics that the narrative puts you through than for the simply enjoyment of the plot. Still, a worthwhile read, and since it鈥檚 actually a novella, you can get through it quickly without a large time commitment.
3.0 stars. Recommended!
November 22, 2024
This mathematical sci-fi novel, Flatland, written over 100 years ago, is more than just science fiction; its "dimension" transcends mathematical space, and it is also a satirical novel of the Victorian era.
Written from the perspective of a "Square" in a 2-dimensional Flatland, the book tells about the social customs and life of Flatland and how the "Square" painfully recognizes the 3-dimensional world when he visits the 3-dimensional space. This reflects the difficulty of our 3-dimensional beings in understanding the 4-dimensional space.
Sounds childish?
But it was written over a 100 years ago, and its ideas were very avant-garde at the time. Flatland is a classic in Western culture, but less discussed in Asian contexts, possibly because the level of sci-fi is not hard enough for modern people, or because the translation has lost a lot of its beauty.
When I first read it, I found it very satirical. It has a strict hierarchy, with "circles" at the top, followed by "polygons", "hexagons", "squares", "equilateral triangles", "isosceles triangles", and finally "line segments" representing women. And it is full of discrimination against women: In Flatland, women have no intellectual power, no forethought, and scarcely any memory. In all houses, there must be special low-level doors for women to enter.
So, this book feels very much like Orwell鈥檚 1984, using an imaginary story to satirize the current society.
Edwin A. Abbott, was a British theologian, educator, and classicist who was good at mathematics and had many mathematician friends. He also published several books on Shakespeare studies and was dedicated to promoting British literature in secondary education. Therefore, in Flatland, there are scattered quotes from Shakespeare. He didn't use quotation marks or footnotes, but simply changed a few words. If you are familiar with Shakespeare, you will admire the appropriateness of these quotations every time you encounter them. However, those without this background will miss a lot of the fun.
For example, he used the pseudonym A. Square for the first edition and narrated it in the first person as Mr. Square. In fact, his original name, Edwin Abbott - Abbott, is exactly "A squared", with the middle name coming from his mother, and his father and mother were relatives with the same surname.
On the cover of the first edition, he even drew a map of Flatland himself, on which it says: "O day and night, but this is wondrous strange", "And therefore as a stranger give it welcome." These 2 lines are from the conversation between Horatio and Hamlet in Hamlet. Note the change from strange to stranger here. Both Shakespeare and Abbott subtly played with the substitution of words to encourage readers to accept strange new things: if friendly people welcome strangers, then they should also accept things that are strange. These two lines are used very cleverly in Flatland: If we friendly welcome strangers from other high - dimensional or low - dimensional worlds, then we should also accept that their worlds are different from ours. In Flatland, Mr. Square met strangers from other "countries" and was able to understand the culture of "other countries".
In the first part introducing Flatland, he quotes from Romeo and Juliet: "Be patient, for the world is broad and wide." - The brilliance of this quote lies in the fact that the setting of Flatland is only 2-dimensional: breadth and width. That is, this sentence is both a lazy sermon and a precise and concrete description. In the second part, Other Worlds (where Mr. Square visits the 3 - dimensional and 1 - dimensional worlds), Abott quotes from The Tempest: "O brave new world, that has such people in it." This is a sentence exclaimed by Miranda when she first saw outsiders after being exiled on the island since childhood. But he changed all the singulars to plurals in Flatland, corresponding to the new worlds of 3 dimensions and even higher dimensions. (This famous quote from Shakespeare also inspired the title of Brave New World, but with a satirical meaning.)
There are also many sentences in Flatland that use alliteration. The mention of shadows vaguely corresponds to Plato's cave: Mr. Square once left the "cave" for the new world, but was arrested and imprisoned as a heretic for propagating new knowledge (returning to the cave again).
In addition to all these cultural bags, Flatland has become a favorite of many, mainly because of its wonderful description of the 2 - dimensional space. Mathematics teachers list it as a reference for the subject and write notes and commentaries on it. The most famous one is Ian Stewart's sequel, Flatterland: Like Flatland, Only More So.
A thought provoking & fun novel.
4.2 / 5 stars.
Written from the perspective of a "Square" in a 2-dimensional Flatland, the book tells about the social customs and life of Flatland and how the "Square" painfully recognizes the 3-dimensional world when he visits the 3-dimensional space. This reflects the difficulty of our 3-dimensional beings in understanding the 4-dimensional space.
Sounds childish?
But it was written over a 100 years ago, and its ideas were very avant-garde at the time. Flatland is a classic in Western culture, but less discussed in Asian contexts, possibly because the level of sci-fi is not hard enough for modern people, or because the translation has lost a lot of its beauty.
When I first read it, I found it very satirical. It has a strict hierarchy, with "circles" at the top, followed by "polygons", "hexagons", "squares", "equilateral triangles", "isosceles triangles", and finally "line segments" representing women. And it is full of discrimination against women: In Flatland, women have no intellectual power, no forethought, and scarcely any memory. In all houses, there must be special low-level doors for women to enter.
So, this book feels very much like Orwell鈥檚 1984, using an imaginary story to satirize the current society.
Edwin A. Abbott, was a British theologian, educator, and classicist who was good at mathematics and had many mathematician friends. He also published several books on Shakespeare studies and was dedicated to promoting British literature in secondary education. Therefore, in Flatland, there are scattered quotes from Shakespeare. He didn't use quotation marks or footnotes, but simply changed a few words. If you are familiar with Shakespeare, you will admire the appropriateness of these quotations every time you encounter them. However, those without this background will miss a lot of the fun.
For example, he used the pseudonym A. Square for the first edition and narrated it in the first person as Mr. Square. In fact, his original name, Edwin Abbott - Abbott, is exactly "A squared", with the middle name coming from his mother, and his father and mother were relatives with the same surname.
On the cover of the first edition, he even drew a map of Flatland himself, on which it says: "O day and night, but this is wondrous strange", "And therefore as a stranger give it welcome." These 2 lines are from the conversation between Horatio and Hamlet in Hamlet. Note the change from strange to stranger here. Both Shakespeare and Abbott subtly played with the substitution of words to encourage readers to accept strange new things: if friendly people welcome strangers, then they should also accept things that are strange. These two lines are used very cleverly in Flatland: If we friendly welcome strangers from other high - dimensional or low - dimensional worlds, then we should also accept that their worlds are different from ours. In Flatland, Mr. Square met strangers from other "countries" and was able to understand the culture of "other countries".
In the first part introducing Flatland, he quotes from Romeo and Juliet: "Be patient, for the world is broad and wide." - The brilliance of this quote lies in the fact that the setting of Flatland is only 2-dimensional: breadth and width. That is, this sentence is both a lazy sermon and a precise and concrete description. In the second part, Other Worlds (where Mr. Square visits the 3 - dimensional and 1 - dimensional worlds), Abott quotes from The Tempest: "O brave new world, that has such people in it." This is a sentence exclaimed by Miranda when she first saw outsiders after being exiled on the island since childhood. But he changed all the singulars to plurals in Flatland, corresponding to the new worlds of 3 dimensions and even higher dimensions. (This famous quote from Shakespeare also inspired the title of Brave New World, but with a satirical meaning.)
There are also many sentences in Flatland that use alliteration. The mention of shadows vaguely corresponds to Plato's cave: Mr. Square once left the "cave" for the new world, but was arrested and imprisoned as a heretic for propagating new knowledge (returning to the cave again).
In addition to all these cultural bags, Flatland has become a favorite of many, mainly because of its wonderful description of the 2 - dimensional space. Mathematics teachers list it as a reference for the subject and write notes and commentaries on it. The most famous one is Ian Stewart's sequel, Flatterland: Like Flatland, Only More So.
A thought provoking & fun novel.
4.2 / 5 stars.
March 28, 2025
I will start my own brief multi-dimensional romance on this book - but dangerously, perhaps, exploring elements of my own experiences out into Spaceland that led me back, like Abbott, to my home-sweet-home of Flatland - with a caveat that I am a rather odd duck.
Being born with ASD didn't help at all.
We Aspies, like Supertramp, always Take the Long Way Home. The prolonged ingenuous Springtime of The Soul. And the soul rejoices in the bright laughter of - as Mallarme says, the "Jeu Supr锚me" - as all reality curls up comfortably at its Ironic Edges.
But the simplicity of higher mathematics in high school soon became in my eyes an overgrown jungle. It was, to me, unworkable, because we Aspies come from a psychological Flatland: to the world, Dullsville.
So my apologies at the outset to my GR friends who were math majors.
No, I took this book at a personal EXISTENTIAL level! So please: take this review very much with a grain of salt!
***
As you probably know, I like to often change the subject. My adventures in Spaceland taught me that when my interlocutors dug deep, their interjections were to me like speeding bullets. I dodged them: I knew they would spell my mediocre death-in-life: I didn't want to go there.
Didn't even want to go to Spaceland - no - but the philosophical skills my teenaged reading skills gave me PUSHED me into a sophisticated outer spaceland.
That sophistication fed my nascent knowledge.
So when I went to college, I explored Spaceland heuristically. And of course - that path leads us into the Den of the Minotaur.
Yikes.
Anyway, after King Minos' foul beast had thoroughly chewed me up and expectorated me... alone, I found myself back home in Flatland!
***
An awakening refused leads back to simplicity, as Abbott found -
And it's where I am now writing this:
In "a state of simplicity (which cost me) not less than EVERYTHING."
And won me Flatland forever...
Flatland - AKA God's Peace - a patient, silent witness to an Ugly World.
I'm my reviews, I'm a precious prima donna who always sings her heart out, and who picks up every last one of the mountains of roses cast atop her.
But in real life I'm a frightfully well-medicated old buzzard of a senior citizen who cherishes every moment of his obscurely FLAT life.
Classic Freudian Wish Fulfilment!
And that's my Secret Life of Walter Mitty.
***
Well, that was my ASD take on this playful novel.
Had I been born a much more scrupulous mathematical man, I would have seen the ironic logic of the book Totally Differently.
So now let's hear, for you more learned folks, a mathematician's explanation of why we are fated to always return to Flatland (a Much better simple take than mine, but then, I dropped Math in High School)!
Being born with ASD didn't help at all.
We Aspies, like Supertramp, always Take the Long Way Home. The prolonged ingenuous Springtime of The Soul. And the soul rejoices in the bright laughter of - as Mallarme says, the "Jeu Supr锚me" - as all reality curls up comfortably at its Ironic Edges.
But the simplicity of higher mathematics in high school soon became in my eyes an overgrown jungle. It was, to me, unworkable, because we Aspies come from a psychological Flatland: to the world, Dullsville.
So my apologies at the outset to my GR friends who were math majors.
No, I took this book at a personal EXISTENTIAL level! So please: take this review very much with a grain of salt!
***
As you probably know, I like to often change the subject. My adventures in Spaceland taught me that when my interlocutors dug deep, their interjections were to me like speeding bullets. I dodged them: I knew they would spell my mediocre death-in-life: I didn't want to go there.
Didn't even want to go to Spaceland - no - but the philosophical skills my teenaged reading skills gave me PUSHED me into a sophisticated outer spaceland.
That sophistication fed my nascent knowledge.
So when I went to college, I explored Spaceland heuristically. And of course - that path leads us into the Den of the Minotaur.
Yikes.
Anyway, after King Minos' foul beast had thoroughly chewed me up and expectorated me... alone, I found myself back home in Flatland!
***
An awakening refused leads back to simplicity, as Abbott found -
And it's where I am now writing this:
In "a state of simplicity (which cost me) not less than EVERYTHING."
And won me Flatland forever...
Flatland - AKA God's Peace - a patient, silent witness to an Ugly World.
I'm my reviews, I'm a precious prima donna who always sings her heart out, and who picks up every last one of the mountains of roses cast atop her.
But in real life I'm a frightfully well-medicated old buzzard of a senior citizen who cherishes every moment of his obscurely FLAT life.
Classic Freudian Wish Fulfilment!
And that's my Secret Life of Walter Mitty.
***
Well, that was my ASD take on this playful novel.
Had I been born a much more scrupulous mathematical man, I would have seen the ironic logic of the book Totally Differently.
So now let's hear, for you more learned folks, a mathematician's explanation of why we are fated to always return to Flatland (a Much better simple take than mine, but then, I dropped Math in High School)!
June 18, 2018
丨噩賲爻鬲丕賳
蹖丕丿丿丕卮鬲蹖 亘乇 丿丕爻鬲丕賳 芦倬禺鬲爻鬲丕賳禄 賳賵卮鬲踿 丕丿賵蹖賳 丕亘賵鬲
卮亘蹖 鬲丕亘爻鬲丕賳蹖 丕丿賵蹖賳 丕亘賵鬲 丿乇 讴鬲丕亘禺丕賳賴 賳卮爻鬲賴 亘賵丿 賵 亘賴 賲爻兀賱賴鈥屰� 亘睾乇賳噩蹖 賮讴乇 賲蹖鈥屭┴必�. 賲爻兀賱賴 丕夭 丕蹖賳 賯乇丕乇 亘賵丿 讴賴 丌蹖丕 賲蹖鈥屫堌з� 亘毓丿蹖 賲讴丕賳蹖 睾蹖乇 丕夭 爻賴 亘毓丿 鬲氐賵乇 讴乇丿 讴賴 丿乇 噩賴鬲蹖 睾蹖乇 丕夭 噩賴丕鬲蹖 讴賴 賲蹖鈥屫促嗀ж驰屬� 丕賲鬲丿丕丿 丿丕卮鬲賴 亘丕卮丿責 賵 丕诏乇 趩賳蹖賳 噩賴丕賳 趩賴丕乇 亘毓丿蹖 賲賲讴賳 亘丕卮丿貙 丿乇 賲賯丕蹖爻賴 亘丕 賲丕 趩賴 卮讴賱蹖 禺賵丕賴丿 丿丕卮鬲責
丿乇 賴賲蹖賳 賮讴乇賴丕 亘賵丿貙 讴賴 賳丕诏賴丕賳 丕鬲賮丕賯 卮诏賮鬲鈥屫з嗂屫槽� 丕賮鬲丕丿. 丿乇 賵爻胤 丕鬲丕賯 賲胤丕賱毓賴鈥屫ж簇� 賳賯胤賴鈥屫й� 倬丿蹖丿 丌賲丿貙 丿乇 賲賯丕亘賱 趩卮賲丕賳 丨蹖乇鬲鈥屫藏団€屫ж� 亘賴 爻乇毓鬲 乇卮丿 讴乇丿貙 亘賴 噩賳蹖賳蹖 亘丿賱 卮丿貙 爻倬爻 讴賵丿讴蹖 卮丿 賵 賳賵噩賵丕賳蹖 賵 噩賵丕賳蹖貙 賵 丿乇 毓乇囟 趩賳丿 孬丕賳蹖賴貙 倬蹖乇賲乇丿蹖 丿乇 賲賯丕亘賱 丕賵 丕蹖爻鬲丕丿賴 亘賵丿.
丕丿賵蹖賳 丕亘賵鬲 賵丨卮鬲鈥屫藏� 賮乇蹖丕丿 讴卮蹖丿 賵 亘賴 賯賮爻賴鈥屰� 讴鬲丕亘鈥屬囏� 趩賳诏 夭丿 鬲丕 禺賵丿卮 乇丕 丕夭 丕賮鬲丕丿賳 賳诏丕賴 丿丕乇丿 賵 趩賳丿 讴鬲丕亘 亘丕 爻乇 賵 氐丿丕 夭賲蹖賳 乇蹖禺鬲. 夭賳卮 丕夭 丕蹖賳 賴賲賴 丿丕丿 賵 賮乇蹖丕丿 賴乇丕爻丕賳 亘賴 丕鬲丕賯 丿賵蹖丿 賵 倬乇爻蹖丿: 芦趩賴 禺亘乇 卮丿賴責禄
丕亘賵鬲 亘蹖 丌賳 讴賴 亘鬲賵丕賳丿 丨乇賮 亘夭賳丿 倬蹖乇賲乇丿 乇丕 賳卮丕賳 丿丕丿 賵 夭賳 讴賴 鬲丕夭賴 賲鬲賵噩賴 丨囟賵乇 倬蹖乇賲乇丿 賲丨鬲乇賲 賵 賲賵賯乇蹖 丿乇 讴鬲丕亘禺丕賳賴鈥屰� 卮賵賴乇卮 卮丿賴 亘賵丿貙 亘丕 乇毓丕蹖鬲 丌丿丕亘 趩賳丿 讴賱賲賴鈥屫й� 亘丕 丕賵 禺賵卮 賵 亘卮 讴乇丿 賵 乇賵 亘賴 丕亘賵鬲 诏賮鬲: 芦丕丿賵蹖賳貙 賳賲蹖鈥屬佡囐呝� 爻亘亘 丕蹖賳 乇賮鬲丕乇 亘丿賵賳 賳夭丕讴鬲 趩蹖爻鬲責 丕夭 丌賯丕蹖 賲丨鬲乇賲 丿毓賵鬲 讴賳 亘賳卮蹖賳丿. 賲賳 賴賲鈥屫и┵嗁堎� 趩丕蹖 賲蹖鈥屫①堌辟�.禄 賵 丕夭 丕鬲丕賯 禺丕乇噩 卮丿.
倬蹖乇賲乇丿 乇賵 讴乇丿 亘賴 丕亘賵鬲貙 讴賴 賴賳賵夭 亘賴 賯賮爻賴 趩賳诏 夭丿賴 亘賵丿貙 賵 诏賮鬲: 芦賲毓匕乇鬲 賲蹖鈥屫堌з囐� 讴賴 丕蹖賳 胤賵乇 馗丕賴乇 卮丿賲. 賴賲蹖卮賴 賵丕乇丿 卮丿賳 亘賴 丨噩賲爻鬲丕賳 丿乇丿爻乇 爻丕夭 丕爻鬲.禄
丕亘賵鬲 亘丕 賱讴賳鬲 诏賮鬲: 芦卮賲丕 讴賴 賴爻鬲蹖丿責禄
芦亘亘禺卮蹖丿貙 賮乇丕賲賵卮 讴乇丿賲 禺賵丿賲 乇丕 賲毓乇賮蹖 讴賳賲. 賲賳 賲鬲賵丕夭蹖 丕賱丕賳爻丕賳 賴爻鬲賲. 丿乇 噩賴丕賳 趩賴丕乇 亘毓丿蹖 讴賴 丕夭 丌賳 賲蹖鈥屫③屬� 賳丕賲 賲賳 丕蹖賳 丕爻鬲.禄
芦賲鬲賵丕夭蹖 丕賱丕賳爻丕賳責禄
芦亘賱賴貙 禺亘 丕蹖賳 胤賵乇 鬲氐賵乇 讴賳蹖丿 讴賴 鬲賲丕賲 賵噩賵丿 卮賲丕 丿乇 噩賴丕賳 爻賴 亘毓丿蹖貙 賮賯胤 蹖讴蹖 丕夭 丕囟賱丕毓 賲丕 丿乇 噩賴丕賳 趩賴丕乇 亘毓丿蹖 丕爻鬲. 賴賲丕賳 胤賵乇 讴賴 鬲賲丕賲 賵噩賵丿 賲乇亘毓 丿乇 噩賴丕賳 丿賵 亘毓丿蹖貙 賮賯胤 蹖讴蹖 丕夭 倬賴賱賵賴丕蹖 賲讴毓亘 丿乇 噩賴丕賳 爻賴 亘毓丿蹖 丕爻鬲. 賲賳 賴賲 趩賵賳 丕夭 丕賳爻丕賳鈥屬囏й屰� 丿賵 亘賴 丿賵 賲鬲賵丕夭蹖 爻丕禺鬲賴 卮丿賴鈥屫з呚� 賲鬲賵丕夭蹖 丕賱丕賳爻丕賳 賳丕賲蹖丿賴 賲蹖鈥屫促堎�.禄
丕亘賵鬲 丿賴丕賳卮 乇丕 趩賳丕賳 亘丕夭 讴乇丿賴 亘賵丿 讴賴 丕賳诏丕乇 丿乇 賳蹖賲賴鈥屫必з� 蹖讴 賳丕爻夭丕 賲鬲賵賯賮 卮丿賴. 倬蹖乇賲乇丿 诏賮鬲: 芦亘蹖丕蹖蹖丿貙 亘诏匕丕乇蹖丿 賳卮丕賳鈥屫з� 丿賴賲.禄 賵 賯亘賱 丕夭 丌賳 讴賴 丕亘賵鬲 亘鬲賵丕賳丿 讴丕乇蹖 亘讴賳丿貙 丿爻鬲 丕賵 乇丕 诏乇賮鬲 賵 丕賵 乇丕 丿乇 噩賴鬲蹖貙 賳賴 亘丕賱丕 賵 倬丕蹖蹖賳貙 賳賴 趩倬 賵 乇丕爻鬲貙 賳賴 丿乇賵賳 賵 亘蹖乇賵賳貙 亘賱讴賴 丿乇 噩賴鬲蹖 亘賴 讴賱蹖 賲鬲賮丕賵鬲 亘賱賳丿 讴乇丿貙 丕夭 噩賴丕賳 爻賴 亘毓丿蹖 亘乇丿丕卮鬲 賵 亘蹖乇賵賳 亘乇丿. 丕亘賵鬲 丕夭 賵丨卮鬲 噩賴丕賳 趩賴丕乇 亘毓丿蹖 蹖讴 亘賳丿 賮乇蹖丕丿 賲蹖鈥屫藏� 賲禺氐賵氐丕賸 賵賯鬲蹖 趩卮賲卮 亘賴 賲蹖賴賲丕賳卮 丕賮鬲丕丿 讴賴 亘賴 卮讴賱蹖 睾蹖乇 賯丕亘賱 鬲賵氐蹖賮貙 丕夭 丕賳爻丕賳鈥屬囏й屰� 丿賵 亘賴 丿賵 賲鬲賵丕夭蹖 爻丕禺鬲賴 卮丿賴 亘賵丿 賵 賴乇 丕賳爻丕賳 亘丕 鬲賲丕賲 爻賴 亘毓丿卮 鬲賳賴丕 蹖讴蹖 丕夭 丕囟賱丕毓 丕賵 乇丕 鬲卮讴蹖賱 賲蹖鈥屫ж�.
賲鬲賵丕夭蹖 丕賱丕賳爻丕賳 氐亘乇 讴乇丿 鬲丕 賵丨卮鬲 丕亘賵鬲 亘賴 丕賳爻 亘丿賱 卮賵丿貙 賵 丌賳 诏丕賴 亘乇丕蹖 丕賵 卮乇丨 丿丕丿 讴賴 趩胤賵乇 丿乇 鬲賲丕賲 丕蹖賳 賲丿鬲 噩賴丕賳蹖 趩賴丕乇 亘毓丿蹖 丿乇爻鬲 噩賱賵蹖 趩卮賲 鬲賲丕賲 丕賴丕賱蹖 丨噩賲爻鬲丕賳 亘賵丿貙 丕賲丕 賴蹖趩 讴爻 爻乇 乇丕 亘賴 噩賴鬲 丿乇爻鬲 賳賲蹖鈥屭必з嗀� 鬲丕 丌賳 乇丕 亘亘蹖賳丿貙 噩賴鬲蹖 睾蹖乇 丕夭 亘丕賱丕 賵 倬丕蹖蹖賳 賵 趩倬 賵 乇丕爻鬲. 賵 丕夭 丕亘賵鬲 禺賵丕爻鬲 讴賴 丿蹖诏乇 丕賴丕賱蹖 丨噩賲爻鬲丕賳 乇丕 丕夭 賵噩賵丿 丕蹖賳 噩賴丕賳 毓馗蹖賲 賲胤賱毓 讴賳丿貙 噩賴丕賳蹖 讴賴 丨噩賲爻鬲丕賳 亘丕 鬲賲丕賲 毓馗賲鬲卮 丿乇 賯蹖丕爻 亘丕 丌賳貙 賴賲趩賵賳 賳賯卮 乇賵蹖 丿蹖賵丕乇 丕爻鬲.
丕亘賵鬲 亘賴 噩賴丕賳 爻賴 亘毓丿蹖 賳诏丕賴 讴乇丿 讴賴 賴賲趩賵賳 賳賯卮 乇賵蹖 丿蹖賵丕乇貙 亘丿賵賳 丨噩賲 亘賴 賳馗乇 賲蹖鈥屫必驰屫�. 丕夭 丌賳 噩丕 賲蹖鈥屫堌з嗀池� 丿丕禺賱 讴鬲丕亘禺丕賳賴鈥屫ж� 乇丕 亘亘蹖賳丿貙 丕賳诏丕乇 讴賴 爻賯賮蹖 亘賴 讴丕乇 賳亘丕卮丿貙 亘丕 丌賳 讴賴 爻賯賮 亘賵丿貙 賵 賴賲爻乇卮 讴賴 爻蹖賳蹖 趩丕蹖 亘賴 丿爻鬲 爻乇诏乇丿丕賳 丿乇 賲蹖丕賳 丕鬲丕賯 丕蹖爻鬲丕丿賴 亘賵丿 賵 爻乇 丿乇 賳賲蹖鈥屫①堌必� 讴賴 賲乇丿賴丕 讴噩丕 乇賮鬲賴鈥屫з嗀�. 诏賮鬲: 芦丕賲丕 賴蹖趩 讴爻 丨乇賮 賲賳 乇丕 丿乇讴 賳禺賵丕賴丿 讴乇丿.禄
賲鬲賵丕夭蹖 丕賱丕賳爻丕賳 诏賮鬲: 芦禺亘 趩乇丕 蹖讴 丿丕爻鬲丕賳 賳賲蹖鈥屬嗁堐屫驰� 鬲丕 賮賴賲卮 乇丕丨鬲鈥屫� 卮賵丿責禄
芦趩賴 丿丕爻鬲丕賳蹖責禄
芦賳賲蹖鈥屫з嗁�. 賲孬賱丕賸 丿丕爻鬲丕賳 蹖讴 賲乇亘毓 爻丕讴賳 噩賴丕賳 丿賵 亘毓丿蹖貙 讴賴 乇賵夭蹖 讴乇賴鈥屫й� 丕夭 噩賴丕賳 爻賴 亘毓丿蹖 丿乇 禺丕賳賴鈥屫ж� 馗丕賴乇 賲蹖鈥屫促堌� 賵 爻毓蹖 賲蹖鈥屭┵嗀� 亘毓丿 爻賵賲 乇丕 亘乇丕蹖 丕賵 鬲賵囟蹖丨 丿賴丿.禄
丕亘賵鬲 亘賴 鬲賲丕賲 趩賳丿 氐丿 趩卮賲 賲鬲賵丕夭蹖 丕賱丕賳爻丕賳 賳诏丕賴 讴乇丿貙 賵 亘賴 賳卮丕賳 倬匕蹖乇卮 爻乇 鬲讴丕賳 丿丕丿. 丕夭 賴賲蹖賳 丨丕賱丕 毓賳賵丕賳 丿丕爻鬲丕賳 乇丕 丕賳鬲禺丕亘 讴乇丿賴 亘賵丿: 芦倬禺鬲爻鬲丕賳禄.
丕蹖賳 蹖丕丿丿丕卮鬲 亘乇丕蹖 爻丕蹖鬲 倬賱丕鬲賵 賳賵卮鬲賴 卮丿賴貙 亘賴 丕蹖賳 丌丿乇爻:
蹖丕丿丿丕卮鬲蹖 亘乇 丿丕爻鬲丕賳 芦倬禺鬲爻鬲丕賳禄 賳賵卮鬲踿 丕丿賵蹖賳 丕亘賵鬲
賲毓乇賮蹖
丕丿賵蹖賳 丕亘賵鬲 乇賲丕賳 倬禺鬲爻鬲丕賳 乇丕 丿乇 爻丕賱 郾鄹鄹鄞 丿乇 丕賳诏賱爻鬲丕賳 丿賵乇丕賳 賵蹖讴鬲賵乇蹖丕 賲賳鬲卮乇 讴乇丿: 丿賵乇丕賳 賳馗丕賲 丕噩鬲賲丕毓蹖 賵 丕禺賱丕賯蹖 禺卮讴貙 賵 丕夭賱蹖鈥屫жㄘ�.
乇賲丕賳 丕夭 丿賵 賮氐賱 鬲卮讴蹖賱 卮丿賴: 丿乇 賮氐賱 丕賵賱 乇丕賵蹖 讴賴 賲乇亘毓蹖 丕夭 丕賴丕賱蹖 倬禺鬲爻鬲丕賳 丕爻鬲 爻乇夭賲蹖賳 丿賵 亘毓丿蹖 禺賵丿 乇丕 鬲賵氐蹖賮 賲蹖鈥屭┵嗀� 卮讴賱 賵 卮賲丕蹖賱 賴賳丿爻蹖 賵 賮蹖夭蹖讴蹖 倬禺鬲爻鬲丕賳貙 丕蹖賳 趩诏賵賳賴 賴賲丿蹖诏乇 乇丕 賲蹖鈥屫ㄛ屬嗁嗀� 賴賲丿蹖诏乇 乇丕 賲蹖鈥屫促嗀ж迟嗀�. 賴賲趩賳蹖賳 丕夭 爻丕禺鬲丕乇 丕噩鬲賲丕毓蹖 賵 爻蹖丕爻蹖 倬禺鬲爻鬲丕賳 賲蹖鈥屭堐屫� 丕禺鬲賱丕賮 胤亘賯丕鬲蹖 賵 鬲賳卮鈥屬囏й� 亘蹖賳 丕卮讴丕賱 賲禺鬲賱賮貙 丕賳賯賱丕亘鈥屬囏� 賵 爻乇讴賵亘鈥屬囏ж� 鬲亘毓蹖囟鈥屬囏й� 噩賳爻蹖鬲蹖貙 賵...
丿乇 賮氐賱 丿賵賲貙 賲乇亘毓 亘乇丕蹖 賳禺爻鬲蹖賳 亘丕乇 亘丕 丿賳蹖丕賴丕蹖 噩丿蹖丿蹖 乇賵 亘賴 乇賵 賲蹖鈥屫促堌� 丿賳蹖丕賴丕蹖蹖 讴賴 丨鬲蹖 鬲氐賵乇卮丕賳 亘乇丕蹖 丕賴丕賱蹖 倬禺鬲爻鬲丕賳 賳丕賲賲讴賳 丕爻鬲 賵 氐丨亘鬲 讴乇丿賳 丕夭 丌賳貙 噩乇賲. 丕诏乇 賮氐賱 丕賵賱 丕賳鬲賯丕丿 丕夭 賵囟毓 讴賳賵賳蹖 丕爻鬲貙 賮氐賱 丿賵賲 乇丕 賲蹖鈥屫堌з� 賳賵蹖丿 丕賲讴丕賳 鬲睾蹖蹖乇 亘賴 賵囟毓蹖 噩丿蹖丿 丿丕賳爻鬲貙 賵囟毓蹖 噩丿蹖丿蹖 讴賴 賴賲賴 賳丕賲賲讴賳卮 賲蹖鈥屫з嗁嗀� 鬲賳賴丕 丕夭 丌賳 噩賴鬲 讴賴 賴賳賵夭 蹖丕丿 賳诏乇賮鬲賴鈥屫з嗀� 亘賴 噩賴鬲 丿乇爻鬲 賳诏丕賴 讴賳賳丿貙 賵 亘賴 賲丨囟 丌賳 讴賴 蹖丕丿 亘诏蹖乇賳丿貙 鬲毓噩亘 禺賵丕賴賳丿 讴乇丿 讴賴 趩胤賵乇 丿乇 鬲賲丕賲 丕蹖賳 賲丿鬲 丕夭 丿蹖丿賳 丌賳 毓丕噩夭 亘賵丿賳丿.
卮亘蹖 鬲丕亘爻鬲丕賳蹖 丕丿賵蹖賳 丕亘賵鬲 丿乇 讴鬲丕亘禺丕賳賴 賳卮爻鬲賴 亘賵丿 賵 亘賴 賲爻兀賱賴鈥屰� 亘睾乇賳噩蹖 賮讴乇 賲蹖鈥屭┴必�. 賲爻兀賱賴 丕夭 丕蹖賳 賯乇丕乇 亘賵丿 讴賴 丌蹖丕 賲蹖鈥屫堌з� 亘毓丿蹖 賲讴丕賳蹖 睾蹖乇 丕夭 爻賴 亘毓丿 鬲氐賵乇 讴乇丿 讴賴 丿乇 噩賴鬲蹖 睾蹖乇 丕夭 噩賴丕鬲蹖 讴賴 賲蹖鈥屫促嗀ж驰屬� 丕賲鬲丿丕丿 丿丕卮鬲賴 亘丕卮丿責 賵 丕诏乇 趩賳蹖賳 噩賴丕賳 趩賴丕乇 亘毓丿蹖 賲賲讴賳 亘丕卮丿貙 丿乇 賲賯丕蹖爻賴 亘丕 賲丕 趩賴 卮讴賱蹖 禺賵丕賴丿 丿丕卮鬲責
丿乇 賴賲蹖賳 賮讴乇賴丕 亘賵丿貙 讴賴 賳丕诏賴丕賳 丕鬲賮丕賯 卮诏賮鬲鈥屫з嗂屫槽� 丕賮鬲丕丿. 丿乇 賵爻胤 丕鬲丕賯 賲胤丕賱毓賴鈥屫ж簇� 賳賯胤賴鈥屫й� 倬丿蹖丿 丌賲丿貙 丿乇 賲賯丕亘賱 趩卮賲丕賳 丨蹖乇鬲鈥屫藏団€屫ж� 亘賴 爻乇毓鬲 乇卮丿 讴乇丿貙 亘賴 噩賳蹖賳蹖 亘丿賱 卮丿貙 爻倬爻 讴賵丿讴蹖 卮丿 賵 賳賵噩賵丕賳蹖 賵 噩賵丕賳蹖貙 賵 丿乇 毓乇囟 趩賳丿 孬丕賳蹖賴貙 倬蹖乇賲乇丿蹖 丿乇 賲賯丕亘賱 丕賵 丕蹖爻鬲丕丿賴 亘賵丿.
丕丿賵蹖賳 丕亘賵鬲 賵丨卮鬲鈥屫藏� 賮乇蹖丕丿 讴卮蹖丿 賵 亘賴 賯賮爻賴鈥屰� 讴鬲丕亘鈥屬囏� 趩賳诏 夭丿 鬲丕 禺賵丿卮 乇丕 丕夭 丕賮鬲丕丿賳 賳诏丕賴 丿丕乇丿 賵 趩賳丿 讴鬲丕亘 亘丕 爻乇 賵 氐丿丕 夭賲蹖賳 乇蹖禺鬲. 夭賳卮 丕夭 丕蹖賳 賴賲賴 丿丕丿 賵 賮乇蹖丕丿 賴乇丕爻丕賳 亘賴 丕鬲丕賯 丿賵蹖丿 賵 倬乇爻蹖丿: 芦趩賴 禺亘乇 卮丿賴責禄
丕亘賵鬲 亘蹖 丌賳 讴賴 亘鬲賵丕賳丿 丨乇賮 亘夭賳丿 倬蹖乇賲乇丿 乇丕 賳卮丕賳 丿丕丿 賵 夭賳 讴賴 鬲丕夭賴 賲鬲賵噩賴 丨囟賵乇 倬蹖乇賲乇丿 賲丨鬲乇賲 賵 賲賵賯乇蹖 丿乇 讴鬲丕亘禺丕賳賴鈥屰� 卮賵賴乇卮 卮丿賴 亘賵丿貙 亘丕 乇毓丕蹖鬲 丌丿丕亘 趩賳丿 讴賱賲賴鈥屫й� 亘丕 丕賵 禺賵卮 賵 亘卮 讴乇丿 賵 乇賵 亘賴 丕亘賵鬲 诏賮鬲: 芦丕丿賵蹖賳貙 賳賲蹖鈥屬佡囐呝� 爻亘亘 丕蹖賳 乇賮鬲丕乇 亘丿賵賳 賳夭丕讴鬲 趩蹖爻鬲責 丕夭 丌賯丕蹖 賲丨鬲乇賲 丿毓賵鬲 讴賳 亘賳卮蹖賳丿. 賲賳 賴賲鈥屫и┵嗁堎� 趩丕蹖 賲蹖鈥屫①堌辟�.禄 賵 丕夭 丕鬲丕賯 禺丕乇噩 卮丿.
倬蹖乇賲乇丿 乇賵 讴乇丿 亘賴 丕亘賵鬲貙 讴賴 賴賳賵夭 亘賴 賯賮爻賴 趩賳诏 夭丿賴 亘賵丿貙 賵 诏賮鬲: 芦賲毓匕乇鬲 賲蹖鈥屫堌з囐� 讴賴 丕蹖賳 胤賵乇 馗丕賴乇 卮丿賲. 賴賲蹖卮賴 賵丕乇丿 卮丿賳 亘賴 丨噩賲爻鬲丕賳 丿乇丿爻乇 爻丕夭 丕爻鬲.禄
丕亘賵鬲 亘丕 賱讴賳鬲 诏賮鬲: 芦卮賲丕 讴賴 賴爻鬲蹖丿責禄
芦亘亘禺卮蹖丿貙 賮乇丕賲賵卮 讴乇丿賲 禺賵丿賲 乇丕 賲毓乇賮蹖 讴賳賲. 賲賳 賲鬲賵丕夭蹖 丕賱丕賳爻丕賳 賴爻鬲賲. 丿乇 噩賴丕賳 趩賴丕乇 亘毓丿蹖 讴賴 丕夭 丌賳 賲蹖鈥屫③屬� 賳丕賲 賲賳 丕蹖賳 丕爻鬲.禄
芦賲鬲賵丕夭蹖 丕賱丕賳爻丕賳責禄
芦亘賱賴貙 禺亘 丕蹖賳 胤賵乇 鬲氐賵乇 讴賳蹖丿 讴賴 鬲賲丕賲 賵噩賵丿 卮賲丕 丿乇 噩賴丕賳 爻賴 亘毓丿蹖貙 賮賯胤 蹖讴蹖 丕夭 丕囟賱丕毓 賲丕 丿乇 噩賴丕賳 趩賴丕乇 亘毓丿蹖 丕爻鬲. 賴賲丕賳 胤賵乇 讴賴 鬲賲丕賲 賵噩賵丿 賲乇亘毓 丿乇 噩賴丕賳 丿賵 亘毓丿蹖貙 賮賯胤 蹖讴蹖 丕夭 倬賴賱賵賴丕蹖 賲讴毓亘 丿乇 噩賴丕賳 爻賴 亘毓丿蹖 丕爻鬲. 賲賳 賴賲 趩賵賳 丕夭 丕賳爻丕賳鈥屬囏й屰� 丿賵 亘賴 丿賵 賲鬲賵丕夭蹖 爻丕禺鬲賴 卮丿賴鈥屫з呚� 賲鬲賵丕夭蹖 丕賱丕賳爻丕賳 賳丕賲蹖丿賴 賲蹖鈥屫促堎�.禄
丕亘賵鬲 丿賴丕賳卮 乇丕 趩賳丕賳 亘丕夭 讴乇丿賴 亘賵丿 讴賴 丕賳诏丕乇 丿乇 賳蹖賲賴鈥屫必з� 蹖讴 賳丕爻夭丕 賲鬲賵賯賮 卮丿賴. 倬蹖乇賲乇丿 诏賮鬲: 芦亘蹖丕蹖蹖丿貙 亘诏匕丕乇蹖丿 賳卮丕賳鈥屫з� 丿賴賲.禄 賵 賯亘賱 丕夭 丌賳 讴賴 丕亘賵鬲 亘鬲賵丕賳丿 讴丕乇蹖 亘讴賳丿貙 丿爻鬲 丕賵 乇丕 诏乇賮鬲 賵 丕賵 乇丕 丿乇 噩賴鬲蹖貙 賳賴 亘丕賱丕 賵 倬丕蹖蹖賳貙 賳賴 趩倬 賵 乇丕爻鬲貙 賳賴 丿乇賵賳 賵 亘蹖乇賵賳貙 亘賱讴賴 丿乇 噩賴鬲蹖 亘賴 讴賱蹖 賲鬲賮丕賵鬲 亘賱賳丿 讴乇丿貙 丕夭 噩賴丕賳 爻賴 亘毓丿蹖 亘乇丿丕卮鬲 賵 亘蹖乇賵賳 亘乇丿. 丕亘賵鬲 丕夭 賵丨卮鬲 噩賴丕賳 趩賴丕乇 亘毓丿蹖 蹖讴 亘賳丿 賮乇蹖丕丿 賲蹖鈥屫藏� 賲禺氐賵氐丕賸 賵賯鬲蹖 趩卮賲卮 亘賴 賲蹖賴賲丕賳卮 丕賮鬲丕丿 讴賴 亘賴 卮讴賱蹖 睾蹖乇 賯丕亘賱 鬲賵氐蹖賮貙 丕夭 丕賳爻丕賳鈥屬囏й屰� 丿賵 亘賴 丿賵 賲鬲賵丕夭蹖 爻丕禺鬲賴 卮丿賴 亘賵丿 賵 賴乇 丕賳爻丕賳 亘丕 鬲賲丕賲 爻賴 亘毓丿卮 鬲賳賴丕 蹖讴蹖 丕夭 丕囟賱丕毓 丕賵 乇丕 鬲卮讴蹖賱 賲蹖鈥屫ж�.
賲鬲賵丕夭蹖 丕賱丕賳爻丕賳 氐亘乇 讴乇丿 鬲丕 賵丨卮鬲 丕亘賵鬲 亘賴 丕賳爻 亘丿賱 卮賵丿貙 賵 丌賳 诏丕賴 亘乇丕蹖 丕賵 卮乇丨 丿丕丿 讴賴 趩胤賵乇 丿乇 鬲賲丕賲 丕蹖賳 賲丿鬲 噩賴丕賳蹖 趩賴丕乇 亘毓丿蹖 丿乇爻鬲 噩賱賵蹖 趩卮賲 鬲賲丕賲 丕賴丕賱蹖 丨噩賲爻鬲丕賳 亘賵丿貙 丕賲丕 賴蹖趩 讴爻 爻乇 乇丕 亘賴 噩賴鬲 丿乇爻鬲 賳賲蹖鈥屭必з嗀� 鬲丕 丌賳 乇丕 亘亘蹖賳丿貙 噩賴鬲蹖 睾蹖乇 丕夭 亘丕賱丕 賵 倬丕蹖蹖賳 賵 趩倬 賵 乇丕爻鬲. 賵 丕夭 丕亘賵鬲 禺賵丕爻鬲 讴賴 丿蹖诏乇 丕賴丕賱蹖 丨噩賲爻鬲丕賳 乇丕 丕夭 賵噩賵丿 丕蹖賳 噩賴丕賳 毓馗蹖賲 賲胤賱毓 讴賳丿貙 噩賴丕賳蹖 讴賴 丨噩賲爻鬲丕賳 亘丕 鬲賲丕賲 毓馗賲鬲卮 丿乇 賯蹖丕爻 亘丕 丌賳貙 賴賲趩賵賳 賳賯卮 乇賵蹖 丿蹖賵丕乇 丕爻鬲.
丕亘賵鬲 亘賴 噩賴丕賳 爻賴 亘毓丿蹖 賳诏丕賴 讴乇丿 讴賴 賴賲趩賵賳 賳賯卮 乇賵蹖 丿蹖賵丕乇貙 亘丿賵賳 丨噩賲 亘賴 賳馗乇 賲蹖鈥屫必驰屫�. 丕夭 丌賳 噩丕 賲蹖鈥屫堌з嗀池� 丿丕禺賱 讴鬲丕亘禺丕賳賴鈥屫ж� 乇丕 亘亘蹖賳丿貙 丕賳诏丕乇 讴賴 爻賯賮蹖 亘賴 讴丕乇 賳亘丕卮丿貙 亘丕 丌賳 讴賴 爻賯賮 亘賵丿貙 賵 賴賲爻乇卮 讴賴 爻蹖賳蹖 趩丕蹖 亘賴 丿爻鬲 爻乇诏乇丿丕賳 丿乇 賲蹖丕賳 丕鬲丕賯 丕蹖爻鬲丕丿賴 亘賵丿 賵 爻乇 丿乇 賳賲蹖鈥屫①堌必� 讴賴 賲乇丿賴丕 讴噩丕 乇賮鬲賴鈥屫з嗀�. 诏賮鬲: 芦丕賲丕 賴蹖趩 讴爻 丨乇賮 賲賳 乇丕 丿乇讴 賳禺賵丕賴丿 讴乇丿.禄
賲鬲賵丕夭蹖 丕賱丕賳爻丕賳 诏賮鬲: 芦禺亘 趩乇丕 蹖讴 丿丕爻鬲丕賳 賳賲蹖鈥屬嗁堐屫驰� 鬲丕 賮賴賲卮 乇丕丨鬲鈥屫� 卮賵丿責禄
芦趩賴 丿丕爻鬲丕賳蹖責禄
芦賳賲蹖鈥屫з嗁�. 賲孬賱丕賸 丿丕爻鬲丕賳 蹖讴 賲乇亘毓 爻丕讴賳 噩賴丕賳 丿賵 亘毓丿蹖貙 讴賴 乇賵夭蹖 讴乇賴鈥屫й� 丕夭 噩賴丕賳 爻賴 亘毓丿蹖 丿乇 禺丕賳賴鈥屫ж� 馗丕賴乇 賲蹖鈥屫促堌� 賵 爻毓蹖 賲蹖鈥屭┵嗀� 亘毓丿 爻賵賲 乇丕 亘乇丕蹖 丕賵 鬲賵囟蹖丨 丿賴丿.禄
丕亘賵鬲 亘賴 鬲賲丕賲 趩賳丿 氐丿 趩卮賲 賲鬲賵丕夭蹖 丕賱丕賳爻丕賳 賳诏丕賴 讴乇丿貙 賵 亘賴 賳卮丕賳 倬匕蹖乇卮 爻乇 鬲讴丕賳 丿丕丿. 丕夭 賴賲蹖賳 丨丕賱丕 毓賳賵丕賳 丿丕爻鬲丕賳 乇丕 丕賳鬲禺丕亘 讴乇丿賴 亘賵丿: 芦倬禺鬲爻鬲丕賳禄.
丕蹖賳 蹖丕丿丿丕卮鬲 亘乇丕蹖 爻丕蹖鬲 倬賱丕鬲賵 賳賵卮鬲賴 卮丿賴貙 亘賴 丕蹖賳 丌丿乇爻:
May 26, 2022
Imagine losing or gaining a spatial dimension
Living in a 3D world, my mind was pleasingly warped when I watched this 7-minute , explaining what a 4D ball would look like in 3D. I sent it to Apatt who likened it to And He Built a Crooked House, which in turn, reminded me of a book I鈥檇 heard of, Flatland.
Reading them one after the other was enjoyably challenging. This is a review, and star rating, of both.
And He Built a Crooked House, by Robert Heinlein
This is an early short story (1941) by a big name in sci-fi. It's about a 4D construction.
Quintus Teal is a young architect who thinks of a house as 鈥�a machine for living, a vital process, a live dynamic thing鈥�. His big idea is to use the fourth spatial dimension to 鈥�put an eight-room house on the land now occupied by a one-room house. Like a tesseract鈥�. He goes on to explain a lot of geometry, and I would have been bemused if I hadn鈥檛 already seen illustrations of what a tesseract, aka hypercube, would look like.
We鈥檙e all familiar with a and its net:
Then add a dimension for a and its net:
For more of an explanation, see video links at the end of this review.
Teal achieves his dream 鈥�by using strong girders and folding money鈥� and takes his friends, Mr and Mrs Bailey to see it.
鈥�That's the grand feature about a tesseract house, complete outside exposure for every room, yet every wall serves two rooms and an eight-room house requires only a one-room foundation.
But four dimensions don鈥檛 fit easily into a three dimensional world, and things become strange. Stranger than any staircases or buildings that drew.
Flatland, by Edwin A Abbott
About a 2D world and published in 1884.
This short book uses geometry as an analogy for a socio-political satire of Victorian attitudes to class and social mobility; gender (in)equality; biological determinism, evolution, and eugenics; religion and the supernatural. It probably works better for those with more knowledge of and interest in the period than I have. Fortunately, my edition had lots of notes, and Abbot included several illustrations.
The key concept is that in a two-dimensional world, a three-dimensional figure is observed as a cross-section. If it's moving, it is seen as a series of cross-sections, and can appear to appear and disappear out of nowhere.
In the first half, the narrator, A Square, explains the very hierarchical social system of the two-dimensional Flatland. The more sides a shape has, and the more regular it is, the higher up the scale it is. 鈥�Delicate females鈥� are are mere lines, 鈥�wholly devoid of brain-power, and have neither reflection, judgement, nor forethought, and hardly any memory鈥�, but Abbot himself was a priest and headmaster who believed in women鈥檚 education, including at university.
The second half has more of a story: 鈥�my initiation into the mysteries of Space鈥� and 鈥�the Gospel of Three Dimensions鈥�. A Square develops a theoretical and then practical understanding of other spatial dimensions. The trouble is, that鈥檚 unimaginable and heretical in Flatland.
The progression of understanding of different spatial dimensions is well explained, with a few illustrations: A square is 鈥�a Line of Lines鈥� and a sphere is 鈥�many Circles in one鈥�. However, Abbott鈥檚 love of initial capital letters was a little distracting, and in part of the second section the language becomes overly Biblical and deferential (thee, thou, My Lord etc).
Image: 鈥淭he Weeping Woman鈥�, in which 鈥淧icasso used cubist forms of fragmentation to depict the face in a series of angular planes鈥�. ()
Clearly explained information about 2D and 4D
To understand the fourth dimension, you need a firm grasp of the zeroth, first, second, and third dimensions. Unless you have a mathematical background, I strongly suggest you watch one or two of these videos before reading either story. I found it helpful to see the same ideas explained in slightly different ways.
鈥� The fourth dimension explained, via second and third, in six minutes, .
鈥� Hypercubes explained and illustrated, without sound, in five minutes, .
鈥� Five-minute TED animation, summarising the story of Flatland and explaining 2D and 4D, .
鈥� Animation of the story of Flatland, narrated by Carl Sagan, in four minutes, .
鈥� Animation of the story of Flatland, made in 1965, eleven minutes, .
鈥� Carl Sagan explains Flatland and goes on to the fourth dimension, in nine minutes, .
The two stories
鈥� You can read Flatland, free, in a variety of digital formats, on Gutenberg, .
鈥� You also can find the text of And He Built a Crooked House online.
Image: 鈥淢r Osborne, may I be excused? My brain is full.鈥� (The Far Side, by )
See also
鈥� If it鈥檚 all too much, there鈥檚 Norton Juster鈥檚 delightful picture book, The Dot and the Line, which I reviewed HERE. I included illustrations and a link to an Oscar-winning animation.
鈥� Malcolm wrote two short stories about very high-tech homes in The Martian Chronicles, which I reviewed HERE. Usher II is a subversive dystopian comedy that's also a tribute to Poe's Fall of the House of Usher. There Will Come Soft Rains starts off almost slapstick, but takes a very tragic turn.
Living in a 3D world, my mind was pleasingly warped when I watched this 7-minute , explaining what a 4D ball would look like in 3D. I sent it to Apatt who likened it to And He Built a Crooked House, which in turn, reminded me of a book I鈥檇 heard of, Flatland.
Reading them one after the other was enjoyably challenging. This is a review, and star rating, of both.
And He Built a Crooked House, by Robert Heinlein
This is an early short story (1941) by a big name in sci-fi. It's about a 4D construction.
Quintus Teal is a young architect who thinks of a house as 鈥�a machine for living, a vital process, a live dynamic thing鈥�. His big idea is to use the fourth spatial dimension to 鈥�put an eight-room house on the land now occupied by a one-room house. Like a tesseract鈥�. He goes on to explain a lot of geometry, and I would have been bemused if I hadn鈥檛 already seen illustrations of what a tesseract, aka hypercube, would look like.
We鈥檙e all familiar with a and its net:
Then add a dimension for a and its net:
For more of an explanation, see video links at the end of this review.
Teal achieves his dream 鈥�by using strong girders and folding money鈥� and takes his friends, Mr and Mrs Bailey to see it.
鈥�That's the grand feature about a tesseract house, complete outside exposure for every room, yet every wall serves two rooms and an eight-room house requires only a one-room foundation.
But four dimensions don鈥檛 fit easily into a three dimensional world, and things become strange. Stranger than any staircases or buildings that drew.
Flatland, by Edwin A Abbott
About a 2D world and published in 1884.
This short book uses geometry as an analogy for a socio-political satire of Victorian attitudes to class and social mobility; gender (in)equality; biological determinism, evolution, and eugenics; religion and the supernatural. It probably works better for those with more knowledge of and interest in the period than I have. Fortunately, my edition had lots of notes, and Abbot included several illustrations.
The key concept is that in a two-dimensional world, a three-dimensional figure is observed as a cross-section. If it's moving, it is seen as a series of cross-sections, and can appear to appear and disappear out of nowhere.
In the first half, the narrator, A Square, explains the very hierarchical social system of the two-dimensional Flatland. The more sides a shape has, and the more regular it is, the higher up the scale it is. 鈥�Delicate females鈥� are are mere lines, 鈥�wholly devoid of brain-power, and have neither reflection, judgement, nor forethought, and hardly any memory鈥�, but Abbot himself was a priest and headmaster who believed in women鈥檚 education, including at university.
The second half has more of a story: 鈥�my initiation into the mysteries of Space鈥� and 鈥�the Gospel of Three Dimensions鈥�. A Square develops a theoretical and then practical understanding of other spatial dimensions. The trouble is, that鈥檚 unimaginable and heretical in Flatland.
The progression of understanding of different spatial dimensions is well explained, with a few illustrations: A square is 鈥�a Line of Lines鈥� and a sphere is 鈥�many Circles in one鈥�. However, Abbott鈥檚 love of initial capital letters was a little distracting, and in part of the second section the language becomes overly Biblical and deferential (thee, thou, My Lord etc).
Image: 鈥淭he Weeping Woman鈥�, in which 鈥淧icasso used cubist forms of fragmentation to depict the face in a series of angular planes鈥�. ()
Clearly explained information about 2D and 4D
To understand the fourth dimension, you need a firm grasp of the zeroth, first, second, and third dimensions. Unless you have a mathematical background, I strongly suggest you watch one or two of these videos before reading either story. I found it helpful to see the same ideas explained in slightly different ways.
鈥� The fourth dimension explained, via second and third, in six minutes, .
鈥� Hypercubes explained and illustrated, without sound, in five minutes, .
鈥� Five-minute TED animation, summarising the story of Flatland and explaining 2D and 4D, .
鈥� Animation of the story of Flatland, narrated by Carl Sagan, in four minutes, .
鈥� Animation of the story of Flatland, made in 1965, eleven minutes, .
鈥� Carl Sagan explains Flatland and goes on to the fourth dimension, in nine minutes, .
The two stories
鈥� You can read Flatland, free, in a variety of digital formats, on Gutenberg, .
鈥� You also can find the text of And He Built a Crooked House online.
Image: 鈥淢r Osborne, may I be excused? My brain is full.鈥� (The Far Side, by )
See also
鈥� If it鈥檚 all too much, there鈥檚 Norton Juster鈥檚 delightful picture book, The Dot and the Line, which I reviewed HERE. I included illustrations and a link to an Oscar-winning animation.
鈥� Malcolm wrote two short stories about very high-tech homes in The Martian Chronicles, which I reviewed HERE. Usher II is a subversive dystopian comedy that's also a tribute to Poe's Fall of the House of Usher. There Will Come Soft Rains starts off almost slapstick, but takes a very tragic turn.
March 23, 2017
A curious little novella about a man a two-dimensional world thinking literally out of the box. First he explains his world in which the angles you have the higher social status you have in Flatland - Circles being the highest rank. He meets someone from Lineland (one-dimensional) who is incapable of understanding Flatland and he meets Sphere from Spaceland (three dimenions) and he is able himself to comprehend the difference between "up" and "North". However, Sphere cannot extrapolate to 4+ dimensions and when the protagonist returns to Flatland and tries to explain Spaceland, he is imprisoned as a heretic.
The text is a social criticism on the rigid thinking of hierarchal social ranks, the dogmatism and often anti-scientific bent of religion, and also has a feminist bent to it as well. A fascinating and mind-bending little book that has not aged a day after almost a century and a half.
The text is a social criticism on the rigid thinking of hierarchal social ranks, the dogmatism and often anti-scientific bent of religion, and also has a feminist bent to it as well. A fascinating and mind-bending little book that has not aged a day after almost a century and a half.
August 18, 2020
Flatland: A Romance of Many Dimensions, Edwin A. Abbott
Flatland: A Romance of Many Dimensions is a satirical novella by the English schoolmaster Edwin Abbott, first published in 1884 by Seeley & Co. of London.
Written pseudonymously by "A Square", the book used the fictional two-dimensional world of Flatland to comment on the hierarchy of Victorian culture, but the novella's more enduring contribution is its examination of dimensions.
The story describes a two-dimensional world occupied by geometric figures, whereof women are simple line-segments, while men are polygons with various numbers of sides.
The narrator is a square, a member of the caste of gentlemen and professionals, who guides the readers through some of the implications of life in two dimensions.
The first half of the story goes through the practicalities of existing in a two-dimensional universe as well as a history leading up to the year 1999 on the eve of the 3rd Millennium.
On New Year's Eve, the Square dreams about a visit to a one-dimensional world (Lineland) inhabited by "lustrous points".
These points are unable to see the Square as anything other than a set of points on a line. Thus, the Square attempts to convince the realm's monarch of a second dimension; but is unable to do so.
In the end, the monarch of Lineland tries to kill A Square rather than tolerate his nonsense any further. ...
毓賳賵丕賳賴丕: 芦倬賭賻禺鬲賽爻鬲丕賳禄貨 芦丕賮爻丕賳賴 蹖 丿賵 亘毓丿蹖禄貨 芦爻乇诏匕卮鬲 夭賲蹖賳 賲爻胤丨: 丿丕爻鬲丕賳 丿賱丿丕丿诏蹖 丕亘毓丕丿 趩賳丿诏丕賳賴禄貨 賳賵蹖爻賳丿賴: 丕丿賵蹖賳 丕亘賵鬲貨 鬲丕乇蹖禺 賳禺爻鬲蹖賳 禺賵丕賳卮 爻丕賱 1997賲蹖賱丕丿蹖
毓賳賵丕賳: 倬賭賻禺鬲賽爻鬲丕賳貨 賳賵蹖爻賳丿賴: 丕丿賵蹖賳 丕亘賵鬲貨 亘丕夭賳诏乇蹖 賵 賲賯丿賲賴 丕夭: 蹖丕賳卮 賴賵賮賲丕賳貨 賲鬲乇噩賲 賲賳賵趩賴乇 丕賳賵乇貨 鬲賴乇丕賳貙 乇賵卮賳诏乇丕賳 賵 賲胤丕賱賴丕鬲 夭賳丕賳貙 1375貨 丿乇 195氐貨 卮丕亘讴 9645512433貨 趩丕倬 丿蹖诏乇 鬲賴乇丕賳貙 讴丕乇賳丕賲賴貙 1388貨 丿乇 172氐貨 卮丕亘讴 9789644310799貨 趩丕倬 丿賵賲 1393貨 賲賵囟賵毓 亘毓丿 趩賴丕乇賲 - 丕夭 賳賵蹖爻賳丿诏丕賳 亘乇蹖鬲丕賳蹖丕蹖蹖 - 爻丿賴 19賲
毓賳賵丕賳: 丕賮爻丕賳賴 蹖 丿賵 亘毓丿蹖貨 賳賵蹖爻賳丿賴: 丕丿賵蹖賳 丕亘賵鬲貨 賲鬲乇噩賲: 噩賱丕賱 噩丕賲毓蹖貨 卮蹖乇丕夭貙 賱賵乇丕貙 1387貙 丿乇 192氐貨 卮丕亘讴 9789648851366貨
毓賳賵丕賳: 爻乇诏匕卮鬲 夭賲蹖賳 賲爻胤丨: 丿丕爻鬲丕賳 丿賱丿丕丿诏蹖 丕亘毓丕丿 趩賳丿诏丕賳賴貨 賳賵蹖爻賳丿賴: 蹖讴 賲乇亘毓 (丕丿賵蹖賳 丕亘賵鬲)貨 亘乇诏乇丿丕賳: 丌賴賳诏 讴賵孬乇貨 卮蹖乇丕夭貙 賳賵蹖丿 卮蹖乇丕夭貙 1397貨 卮丕亘讴 9786001927768貨
倬賻禺鬲爻鬲丕賳: 乇賲丕賳 亘購毓丿賴丕蹖 亘爻蹖丕乇貙 乇賲丕賳 讴賵鬲丕賴蹖 丕夭 丕賱賴蹖鈥屫з� 賵 丕爻鬲丕丿 丿丕賳卮诏丕賴 丕賳诏賱蹖爻蹖貙 芦丕丿賵蹖賳 丕亘賵鬲禄 丕爻鬲貙 讴賴 賳禺爻鬲蹖賳鈥屫ㄘж� 丌賳鈥屫必� 丿乇 爻丕賱 1884賲蹖賱丕丿蹖 亘丕 賳丕賲 賲爻鬲毓丕乇 賳賵蹖爻賳丿诏蹖 芦蹖讴 賲乇亘毓禄 賲賳鬲卮乇 讴乇丿賳丿貨 丿乇 丕蹖賳 讴鬲丕亘 丕夭 丿賳蹖丕蹖 禺蹖丕賱蹖 芦丿賵亘購毓丿蹖 倬賻禺鬲爻鬲丕賳禄貙 亘乇丕蹖 賳卮丕賳 丿丕丿賳 賮乇賴賳诏 爻賱爻賱賴鈥� 賲乇丕鬲亘蹖 芦丕賳诏賱爻鬲丕賳禄 丿賵乇賴 蹖 芦賵蹖讴鬲賵乇蹖丕禄 丕爻鬲賮丕丿賴 卮丿賴鈥� 丕爻鬲.貨 丕蹖賳 賳诏丕乇賴 亘蹖卮鬲乇 蹖讴 鬲賲孬蹖賱 毓亘乇鬲鈥� 丌賲賵夭 丕爻鬲貙 鬲丕 蹖讴 丿丕爻鬲丕賳貨 賵 賳蹖夭 賳賯丿蹖 鬲賳丿 賵 诏夭賳丿賴貙 丕夭 爻丕禺鬲丕乇 丕噩鬲賲丕毓蹖 賵 爻蹖丕爻蹖 噩丕賲毓賴 蹖 乇賵夭诏丕乇 禺賵丿貙 賵 丕乇夭卮鈥屬囏ж� 賵 乇賵丕亘胤 丕賳爻丕賳蹖 丿乇 丌賳 丕爻鬲貨 芦丕亘賵鬲禄 亘乇丕蹖 丕蹖賳讴賴 賳卮丕賳 丿賴丿貙 丕賳爻丕賳鈥屬囏� 丿乇 丕蹖賳 丿賳蹖丕 丕夭 賳馗乇 丕賮賯 丿丕賳卮 賵 亘蹖賳卮貙 丿乇 趩賴 賯賮爻 鬲賳诏蹖 诏乇賮鬲丕乇 賴爻鬲賳丿貙 丕夭 噩賴丕賳蹖 禺蹖丕賱蹖 亘丕 亘丕卮賳丿诏丕賳蹖 丿賵 亘購毓丿蹖 爻賵丿 亘乇丿賴 丕爻鬲.貨 丕蹖賳 亘丕卮賳丿诏丕賳 丿丕乇丕蹖 卮讴賱鈥屬囏й� 賴賳丿爻蹖 芦賲孬賱孬禄貙 芦賲乇亘毓禄貙 芦倬賳噩鈥屫ㄘ甭回� 芦卮卮鈥屫ㄘ甭� 賵 芦亘丕賱丕 賵 亘丕賱丕鬲乇禄 鬲丕 芦丿丕蹖乇賴鈥屄� 賴爻鬲賳丿貙 讴賴 賳丕诏夭蹖乇 丿乇 爻胤丨 賲蹖鈥屫槽屬嗀�.貨 賳賵蹖爻賳丿賴 賵 乇丕賵蹖 丿丕爻鬲丕賳貙 蹖讴 賲乇亘毓 丕爻鬲貙 讴賴 丕蹖賳 丿賳蹖丕 乇丕 卮乇丨 賲蹖鈥屫囏�.貨 芦倬賻禺鬲爻鬲丕賳禄 丿乇 夭賲丕賳 丕賳鬲卮丕乇 禺賵丿貙 賲賵乇丿 鬲賵噩賴 賯乇丕乇 賳诏乇賮鬲貙 倬爻 丕夭 丕賳鬲卮丕乇 賳馗乇蹖賴 蹖 賳爻亘蹖鬲 毓丕賲 丕賳蹖卮鬲蹖賳貙 丕蹖賳 讴鬲丕亘 丿賵亘丕乇賴 亘賴 蹖丕丿 賴賲诏丕賳 丕賮鬲丕丿貙 趩乇丕 讴賴 丿乇 丌賳 亘賴 賲賮賴賵賲 芦亘購毓丿 趩賴丕乇賲禄 賳蹖夭 丕卮丕乇賴 卮丿賴 亘賵丿.貨 丿乇 賲賯丕賱賴鈥� 丕蹖 鬲丨鬲 毓賳賵丕賳 芦丕賯賱蹖丿爻貙 賳蹖賵鬲賳 賵 丕賳蹖卮鬲蹖賳禄貙 讴賴 丿乇 卮賲丕乇賴贁 丿賵丕夭丿賴賲 賲丕賴 賮賵乇蹖賴 爻丕賱 1920賲蹖賱丕丿蹖 賲噩賱賴 蹖 芦賳蹖趩乇禄 賲賳鬲卮乇 卮丿貙 丕夭 丕蹖賳 讴鬲丕亘 賳丕賲 亘乇丿賴 卮丿貙 賵 芦丕亘賵鬲禄 乇丕 丕夭 蹖讴 賳馗乇 賴賲趩賵賳 倬蹖丕賲亘乇蹖 丿丕賳爻鬲貙 讴賴 丿乇 丌賳 夭賲丕賳 亘賴 丿乇讴 丕賴賲蹖鬲 夭賲丕賳貙 丿乇 卮乇丨 蹖讴 倬丿蹖丿賴貙 丌诏丕賴 亘賵丿賴鈥� 丕爻鬲.貨 丕賳鬲卮丕乇丕鬲 芦賴丕乇倬乇讴丕賱蹖賳夭禄 丿乇 爻丕賱 1983賲蹖賱丕丿蹖貙 賳爻禺賴鈥� 丕蹖 丕夭 丕蹖賳 讴鬲丕亘 乇丕 亘丕 倬蹖卮诏賮鬲丕乇 芦丌蹖夭丕讴 丌爻蹖賲賵賮禄 賲賳鬲卮乇 讴乇丿.貨 毓賳賵丕賳 芦倬賻禺鬲爻鬲丕賳禄 乇丕貙 賲鬲乇噩賲 賳禺爻鬲 丕蹖賳 讴鬲丕亘貙 噩賳丕亘 芦賲賳賵趩賴乇 丕賳賵乇禄貙 亘乇丕蹖 丌賳 亘乇诏夭蹖丿賳丿貙 讴賴 丕夭 賵丕跇賴 蹖 賮丕乇爻蹖 芦倬賻禺鬲禄 亘賴 賲毓賳丕蹖 芦倬賴賳禄 賵 亘蹖鈥屫ㄘ必池屫� 賵 倬爻賵賳丿 爻鬲丕賳 鬲卮讴蹖賱 卮丿賴鈥� 丕爻鬲.貨
鬲丕乇蹖禺 亘賴賳诏丕賲 乇爻丕賳蹖 27/05/1399賴噩乇蹖 禺賵乇卮蹖丿蹖貨 丕. 卮乇亘蹖丕賳蹖
Flatland: A Romance of Many Dimensions is a satirical novella by the English schoolmaster Edwin Abbott, first published in 1884 by Seeley & Co. of London.
Written pseudonymously by "A Square", the book used the fictional two-dimensional world of Flatland to comment on the hierarchy of Victorian culture, but the novella's more enduring contribution is its examination of dimensions.
The story describes a two-dimensional world occupied by geometric figures, whereof women are simple line-segments, while men are polygons with various numbers of sides.
The narrator is a square, a member of the caste of gentlemen and professionals, who guides the readers through some of the implications of life in two dimensions.
The first half of the story goes through the practicalities of existing in a two-dimensional universe as well as a history leading up to the year 1999 on the eve of the 3rd Millennium.
On New Year's Eve, the Square dreams about a visit to a one-dimensional world (Lineland) inhabited by "lustrous points".
These points are unable to see the Square as anything other than a set of points on a line. Thus, the Square attempts to convince the realm's monarch of a second dimension; but is unable to do so.
In the end, the monarch of Lineland tries to kill A Square rather than tolerate his nonsense any further. ...
毓賳賵丕賳賴丕: 芦倬賭賻禺鬲賽爻鬲丕賳禄貨 芦丕賮爻丕賳賴 蹖 丿賵 亘毓丿蹖禄貨 芦爻乇诏匕卮鬲 夭賲蹖賳 賲爻胤丨: 丿丕爻鬲丕賳 丿賱丿丕丿诏蹖 丕亘毓丕丿 趩賳丿诏丕賳賴禄貨 賳賵蹖爻賳丿賴: 丕丿賵蹖賳 丕亘賵鬲貨 鬲丕乇蹖禺 賳禺爻鬲蹖賳 禺賵丕賳卮 爻丕賱 1997賲蹖賱丕丿蹖
毓賳賵丕賳: 倬賭賻禺鬲賽爻鬲丕賳貨 賳賵蹖爻賳丿賴: 丕丿賵蹖賳 丕亘賵鬲貨 亘丕夭賳诏乇蹖 賵 賲賯丿賲賴 丕夭: 蹖丕賳卮 賴賵賮賲丕賳貨 賲鬲乇噩賲 賲賳賵趩賴乇 丕賳賵乇貨 鬲賴乇丕賳貙 乇賵卮賳诏乇丕賳 賵 賲胤丕賱賴丕鬲 夭賳丕賳貙 1375貨 丿乇 195氐貨 卮丕亘讴 9645512433貨 趩丕倬 丿蹖诏乇 鬲賴乇丕賳貙 讴丕乇賳丕賲賴貙 1388貨 丿乇 172氐貨 卮丕亘讴 9789644310799貨 趩丕倬 丿賵賲 1393貨 賲賵囟賵毓 亘毓丿 趩賴丕乇賲 - 丕夭 賳賵蹖爻賳丿诏丕賳 亘乇蹖鬲丕賳蹖丕蹖蹖 - 爻丿賴 19賲
毓賳賵丕賳: 丕賮爻丕賳賴 蹖 丿賵 亘毓丿蹖貨 賳賵蹖爻賳丿賴: 丕丿賵蹖賳 丕亘賵鬲貨 賲鬲乇噩賲: 噩賱丕賱 噩丕賲毓蹖貨 卮蹖乇丕夭貙 賱賵乇丕貙 1387貙 丿乇 192氐貨 卮丕亘讴 9789648851366貨
毓賳賵丕賳: 爻乇诏匕卮鬲 夭賲蹖賳 賲爻胤丨: 丿丕爻鬲丕賳 丿賱丿丕丿诏蹖 丕亘毓丕丿 趩賳丿诏丕賳賴貨 賳賵蹖爻賳丿賴: 蹖讴 賲乇亘毓 (丕丿賵蹖賳 丕亘賵鬲)貨 亘乇诏乇丿丕賳: 丌賴賳诏 讴賵孬乇貨 卮蹖乇丕夭貙 賳賵蹖丿 卮蹖乇丕夭貙 1397貨 卮丕亘讴 9786001927768貨
倬賻禺鬲爻鬲丕賳: 乇賲丕賳 亘購毓丿賴丕蹖 亘爻蹖丕乇貙 乇賲丕賳 讴賵鬲丕賴蹖 丕夭 丕賱賴蹖鈥屫з� 賵 丕爻鬲丕丿 丿丕賳卮诏丕賴 丕賳诏賱蹖爻蹖貙 芦丕丿賵蹖賳 丕亘賵鬲禄 丕爻鬲貙 讴賴 賳禺爻鬲蹖賳鈥屫ㄘж� 丌賳鈥屫必� 丿乇 爻丕賱 1884賲蹖賱丕丿蹖 亘丕 賳丕賲 賲爻鬲毓丕乇 賳賵蹖爻賳丿诏蹖 芦蹖讴 賲乇亘毓禄 賲賳鬲卮乇 讴乇丿賳丿貨 丿乇 丕蹖賳 讴鬲丕亘 丕夭 丿賳蹖丕蹖 禺蹖丕賱蹖 芦丿賵亘購毓丿蹖 倬賻禺鬲爻鬲丕賳禄貙 亘乇丕蹖 賳卮丕賳 丿丕丿賳 賮乇賴賳诏 爻賱爻賱賴鈥� 賲乇丕鬲亘蹖 芦丕賳诏賱爻鬲丕賳禄 丿賵乇賴 蹖 芦賵蹖讴鬲賵乇蹖丕禄 丕爻鬲賮丕丿賴 卮丿賴鈥� 丕爻鬲.貨 丕蹖賳 賳诏丕乇賴 亘蹖卮鬲乇 蹖讴 鬲賲孬蹖賱 毓亘乇鬲鈥� 丌賲賵夭 丕爻鬲貙 鬲丕 蹖讴 丿丕爻鬲丕賳貨 賵 賳蹖夭 賳賯丿蹖 鬲賳丿 賵 诏夭賳丿賴貙 丕夭 爻丕禺鬲丕乇 丕噩鬲賲丕毓蹖 賵 爻蹖丕爻蹖 噩丕賲毓賴 蹖 乇賵夭诏丕乇 禺賵丿貙 賵 丕乇夭卮鈥屬囏ж� 賵 乇賵丕亘胤 丕賳爻丕賳蹖 丿乇 丌賳 丕爻鬲貨 芦丕亘賵鬲禄 亘乇丕蹖 丕蹖賳讴賴 賳卮丕賳 丿賴丿貙 丕賳爻丕賳鈥屬囏� 丿乇 丕蹖賳 丿賳蹖丕 丕夭 賳馗乇 丕賮賯 丿丕賳卮 賵 亘蹖賳卮貙 丿乇 趩賴 賯賮爻 鬲賳诏蹖 诏乇賮鬲丕乇 賴爻鬲賳丿貙 丕夭 噩賴丕賳蹖 禺蹖丕賱蹖 亘丕 亘丕卮賳丿诏丕賳蹖 丿賵 亘購毓丿蹖 爻賵丿 亘乇丿賴 丕爻鬲.貨 丕蹖賳 亘丕卮賳丿诏丕賳 丿丕乇丕蹖 卮讴賱鈥屬囏й� 賴賳丿爻蹖 芦賲孬賱孬禄貙 芦賲乇亘毓禄貙 芦倬賳噩鈥屫ㄘ甭回� 芦卮卮鈥屫ㄘ甭� 賵 芦亘丕賱丕 賵 亘丕賱丕鬲乇禄 鬲丕 芦丿丕蹖乇賴鈥屄� 賴爻鬲賳丿貙 讴賴 賳丕诏夭蹖乇 丿乇 爻胤丨 賲蹖鈥屫槽屬嗀�.貨 賳賵蹖爻賳丿賴 賵 乇丕賵蹖 丿丕爻鬲丕賳貙 蹖讴 賲乇亘毓 丕爻鬲貙 讴賴 丕蹖賳 丿賳蹖丕 乇丕 卮乇丨 賲蹖鈥屫囏�.貨 芦倬賻禺鬲爻鬲丕賳禄 丿乇 夭賲丕賳 丕賳鬲卮丕乇 禺賵丿貙 賲賵乇丿 鬲賵噩賴 賯乇丕乇 賳诏乇賮鬲貙 倬爻 丕夭 丕賳鬲卮丕乇 賳馗乇蹖賴 蹖 賳爻亘蹖鬲 毓丕賲 丕賳蹖卮鬲蹖賳貙 丕蹖賳 讴鬲丕亘 丿賵亘丕乇賴 亘賴 蹖丕丿 賴賲诏丕賳 丕賮鬲丕丿貙 趩乇丕 讴賴 丿乇 丌賳 亘賴 賲賮賴賵賲 芦亘購毓丿 趩賴丕乇賲禄 賳蹖夭 丕卮丕乇賴 卮丿賴 亘賵丿.貨 丿乇 賲賯丕賱賴鈥� 丕蹖 鬲丨鬲 毓賳賵丕賳 芦丕賯賱蹖丿爻貙 賳蹖賵鬲賳 賵 丕賳蹖卮鬲蹖賳禄貙 讴賴 丿乇 卮賲丕乇賴贁 丿賵丕夭丿賴賲 賲丕賴 賮賵乇蹖賴 爻丕賱 1920賲蹖賱丕丿蹖 賲噩賱賴 蹖 芦賳蹖趩乇禄 賲賳鬲卮乇 卮丿貙 丕夭 丕蹖賳 讴鬲丕亘 賳丕賲 亘乇丿賴 卮丿貙 賵 芦丕亘賵鬲禄 乇丕 丕夭 蹖讴 賳馗乇 賴賲趩賵賳 倬蹖丕賲亘乇蹖 丿丕賳爻鬲貙 讴賴 丿乇 丌賳 夭賲丕賳 亘賴 丿乇讴 丕賴賲蹖鬲 夭賲丕賳貙 丿乇 卮乇丨 蹖讴 倬丿蹖丿賴貙 丌诏丕賴 亘賵丿賴鈥� 丕爻鬲.貨 丕賳鬲卮丕乇丕鬲 芦賴丕乇倬乇讴丕賱蹖賳夭禄 丿乇 爻丕賱 1983賲蹖賱丕丿蹖貙 賳爻禺賴鈥� 丕蹖 丕夭 丕蹖賳 讴鬲丕亘 乇丕 亘丕 倬蹖卮诏賮鬲丕乇 芦丌蹖夭丕讴 丌爻蹖賲賵賮禄 賲賳鬲卮乇 讴乇丿.貨 毓賳賵丕賳 芦倬賻禺鬲爻鬲丕賳禄 乇丕貙 賲鬲乇噩賲 賳禺爻鬲 丕蹖賳 讴鬲丕亘貙 噩賳丕亘 芦賲賳賵趩賴乇 丕賳賵乇禄貙 亘乇丕蹖 丌賳 亘乇诏夭蹖丿賳丿貙 讴賴 丕夭 賵丕跇賴 蹖 賮丕乇爻蹖 芦倬賻禺鬲禄 亘賴 賲毓賳丕蹖 芦倬賴賳禄 賵 亘蹖鈥屫ㄘ必池屫� 賵 倬爻賵賳丿 爻鬲丕賳 鬲卮讴蹖賱 卮丿賴鈥� 丕爻鬲.貨
鬲丕乇蹖禺 亘賴賳诏丕賲 乇爻丕賳蹖 27/05/1399賴噩乇蹖 禺賵乇卮蹖丿蹖貨 丕. 卮乇亘蹖丕賳蹖
January 4, 2009
This book should not be read in hopes of finding an entertaining story. As a novel, it's terrible. It's plot (if you can call it that) is simple and contrived. But, it wasn't written as a novel.
Flatland is a mathematical essay, meant to explain a point: that higher dimensions (more than length, depth and width) may be present in our universe, but if they are, it will be nearly impossible for us to understand them.
The story itself consists of a two dimensional world (Flatland), in which there are people of assorted shapes. These shapes live regular lives, just as we do. The protagonist (a square), is visited by a sphere, which tries to explain to him the existence of a third dimension. This proves difficult, though, because to the square in flatland, the sphere appears to be nothing more than a circle that can expand, contract, disappear and reappear.
In the course of the explanation, the book also describes "Lineland," a one dimensional world where the inhabitants would also have trouble understanding dimensions above their own.
This book's excellence lies in the way it takes a complex topic and breaks it down into a metaphor that can be more easily understood. It argues quite well that if there is a fourth dimension, it probably isn't "time."
This book isn't one that will win wide-spread acclaim from the general reading community. For those of us who enjoy higher math, though, it's excellent.
Flatland is a mathematical essay, meant to explain a point: that higher dimensions (more than length, depth and width) may be present in our universe, but if they are, it will be nearly impossible for us to understand them.
The story itself consists of a two dimensional world (Flatland), in which there are people of assorted shapes. These shapes live regular lives, just as we do. The protagonist (a square), is visited by a sphere, which tries to explain to him the existence of a third dimension. This proves difficult, though, because to the square in flatland, the sphere appears to be nothing more than a circle that can expand, contract, disappear and reappear.
In the course of the explanation, the book also describes "Lineland," a one dimensional world where the inhabitants would also have trouble understanding dimensions above their own.
This book's excellence lies in the way it takes a complex topic and breaks it down into a metaphor that can be more easily understood. It argues quite well that if there is a fourth dimension, it probably isn't "time."
This book isn't one that will win wide-spread acclaim from the general reading community. For those of us who enjoy higher math, though, it's excellent.
April 6, 2017
鈥淚 used to be a renegade, I used to fool around
But I couldn't take the punishment and had to settle down
Now I'm playing it real straight, and yes, I cut my hair
You might think I'm crazy, but I don't even care
Because I can tell what's going on
It's hip to be square鈥�
According to IMDB, several film adaptations have been made of Flatland, but no blockbusting Pixar / DreamWorks extravaganza just yet. If they do make one I can鈥檛 imagine a more appropriate theme song than the above Huey Lewis And The News number.
Flatland is set in a two-dimensional world and narrated in the first person by a square (or 鈥淎 Square鈥� as appears on the original edition鈥檚 book cover). In the first half of the book Square gives us a tour of his world where women are straight lines and, if you are symmetrical, the more sides you have the better. This means that circles are the elite of this society because they are really polygons with zillions of super tiny sides. Irregular polygons are abominations and isosceles are plebeians.
Special laws are applied to women because they are capable of accidentally stabbing people to death due to their pointiness. Use of colours is banned because they can be used as disguises. How these geometric persons move around without legs is deliberately left unexplained (with a bit of "lampshading"). The second half of the book tells the remarkable story of Square鈥檚 adventures in lands of different dimensions, one, three and even zero (no trip to the fourth dimension, though; no time, probably). Guided by an enigmatic Sphere who seems to have popped up out of nowhere (and who Square initially mistook to be a circle), these trips to other planes of existence enables Square to not only think outside the box but to introduce him to the existence of boxes. This was a steep learning curve for him but he adapts like a champ and becomes a more rounded individual because of it.
Flatland is a very odd novella it is part allegory, part satire, part geometry lessons, part spec fic. I generally avoid reading geometry books because they are full of problems I don鈥檛 want to consider (screw the hypotenuse, man!). However, for Flatland I don鈥檛 mind making an exception, for once I find the flat characters entirely acceptable and even find the more apparently rounded character to be arrogant and clearly obtuse in their outlook, if not in appearance. The satirical look at the class system makes this all too real issue painfully acute. One thing that blows my mind a bit is that prior to reading the book I visualized it as a story of different geometric shapes moving around going about their business. However, the denizens of the Flatland cannot actually see these different shapes. As the Square (or Edwin Abbott Abbott) mentions early in the book you have to imagine looking at these shapes with your line of sight on the same level as their surface. Mr. Abbott explains it very clearly as follows:
鈥淧lace a penny on the middle of one of your tables in Space; and leaning over it, look down upon it. It will appear a circle. But now, drawing back to the edge of the table, gradually lower your eye (thus bringing yourself more and more into the condition of the inhabitants of Flatland), and you will find the penny becoming more and more oval to your view, and at last when you have placed your eye exactly on the edge of the table (so that you are, as it were, actually a Flatlander) the penny will then have ceased to appear oval at all, and will have become, so far as you can see, a straight line.鈥�
So all they really ever see is straight lines of different lengths, however, they can distinguish the different geometrical shapes by hearing, by touch (done by the working class only), and by sight with the aid of fog for estimating depths (different angles appear to fade differently into fog). In the one-dimensional Lineland everybody looks like a point and sideways movement is impossible; as for the zero-dimensional Pointland, there is only one denizen and he is weird!
I really enjoyed Flatland, it is bizarre and thought-provoking; it definitely gave me a new perspective on life. The treatment of women may seem a little sexist but E.A. Abbott is perhaps satirizing sexism rather than perpetuating it. I definitely recommend you read Flatland before you flatline.
Notes:
鈥� Audiobook credit: Wonderfully read for Librovox (i.e. free) by Ruth Golding.
鈥� There are quite a few diagrams scattered over the book, drawn by AbbottX2 himself, they illustrate the geometrical concepts nicely. These should be in all editions as they are intrinsic to the story.
鈥� There is one error in the book where Square mentions a cellar: 鈥淪o I endeavoured to reassure her by some story, invented for the occasion, that I had accidentally fallen through the trap-door of the cellar, and had there lain stunned.鈥�. You can't have a bloody cellar if you only have two dimensions and you can鈥檛 鈥渇all through鈥� anything.
鈥� Another error (I think) is the existence of cupboards in Flatland. If there is no depth or verticality you can't have cupboards!
鈥� The 3D world is called Spaceland, it is not our world. Their most popular singer is probably Britney Sphere. (汀掳 蜏蕱 汀掳)
鈥� I initially thought this book was a collaboration between two abbots.
Quotes:
Yet even in our best regulated and most approximately Circular families I cannot say that the ideal of family life is so high as with you in Spaceland. There is peace, in so far as the absence of slaughter may be called by that name.
In a word, to comport oneself with perfect propriety in Polygonal society, one ought to be a Polygon oneself. Such at least is the painful teaching of my experience.
Doubtless, the life of an Irregular is hard; but the interests of the Greater Number require that it shall be hard. If a man with a triangular front and a polygonal back were allowed to exist and to propagate a still more Irregular posterity, what would become of the arts of life?
You, who are blessed with shade as well as light, you, who are gifted with two eyes, endowed with a knowledge of perspective, and charmed with the enjoyment of various colours, you, who can actually SEE an angle, and contemplate the complete circumference of a circle in the happy region of the Three Dimensions鈥攈ow shall I make clear to you the extreme difficulty which we in Flatland experience in recognizing one another's configuration?
Hipster Square
But I couldn't take the punishment and had to settle down
Now I'm playing it real straight, and yes, I cut my hair
You might think I'm crazy, but I don't even care
Because I can tell what's going on
It's hip to be square鈥�
According to IMDB, several film adaptations have been made of Flatland, but no blockbusting Pixar / DreamWorks extravaganza just yet. If they do make one I can鈥檛 imagine a more appropriate theme song than the above Huey Lewis And The News number.
Flatland is set in a two-dimensional world and narrated in the first person by a square (or 鈥淎 Square鈥� as appears on the original edition鈥檚 book cover). In the first half of the book Square gives us a tour of his world where women are straight lines and, if you are symmetrical, the more sides you have the better. This means that circles are the elite of this society because they are really polygons with zillions of super tiny sides. Irregular polygons are abominations and isosceles are plebeians.
Special laws are applied to women because they are capable of accidentally stabbing people to death due to their pointiness. Use of colours is banned because they can be used as disguises. How these geometric persons move around without legs is deliberately left unexplained (with a bit of "lampshading"). The second half of the book tells the remarkable story of Square鈥檚 adventures in lands of different dimensions, one, three and even zero (no trip to the fourth dimension, though; no time, probably). Guided by an enigmatic Sphere who seems to have popped up out of nowhere (and who Square initially mistook to be a circle), these trips to other planes of existence enables Square to not only think outside the box but to introduce him to the existence of boxes. This was a steep learning curve for him but he adapts like a champ and becomes a more rounded individual because of it.
Flatland is a very odd novella it is part allegory, part satire, part geometry lessons, part spec fic. I generally avoid reading geometry books because they are full of problems I don鈥檛 want to consider (screw the hypotenuse, man!). However, for Flatland I don鈥檛 mind making an exception, for once I find the flat characters entirely acceptable and even find the more apparently rounded character to be arrogant and clearly obtuse in their outlook, if not in appearance. The satirical look at the class system makes this all too real issue painfully acute. One thing that blows my mind a bit is that prior to reading the book I visualized it as a story of different geometric shapes moving around going about their business. However, the denizens of the Flatland cannot actually see these different shapes. As the Square (or Edwin Abbott Abbott) mentions early in the book you have to imagine looking at these shapes with your line of sight on the same level as their surface. Mr. Abbott explains it very clearly as follows:
鈥淧lace a penny on the middle of one of your tables in Space; and leaning over it, look down upon it. It will appear a circle. But now, drawing back to the edge of the table, gradually lower your eye (thus bringing yourself more and more into the condition of the inhabitants of Flatland), and you will find the penny becoming more and more oval to your view, and at last when you have placed your eye exactly on the edge of the table (so that you are, as it were, actually a Flatlander) the penny will then have ceased to appear oval at all, and will have become, so far as you can see, a straight line.鈥�
So all they really ever see is straight lines of different lengths, however, they can distinguish the different geometrical shapes by hearing, by touch (done by the working class only), and by sight with the aid of fog for estimating depths (different angles appear to fade differently into fog). In the one-dimensional Lineland everybody looks like a point and sideways movement is impossible; as for the zero-dimensional Pointland, there is only one denizen and he is weird!
I really enjoyed Flatland, it is bizarre and thought-provoking; it definitely gave me a new perspective on life. The treatment of women may seem a little sexist but E.A. Abbott is perhaps satirizing sexism rather than perpetuating it. I definitely recommend you read Flatland before you flatline.
Notes:
鈥� Audiobook credit: Wonderfully read for Librovox (i.e. free) by Ruth Golding.
鈥� There are quite a few diagrams scattered over the book, drawn by AbbottX2 himself, they illustrate the geometrical concepts nicely. These should be in all editions as they are intrinsic to the story.
鈥� There is one error in the book where Square mentions a cellar: 鈥淪o I endeavoured to reassure her by some story, invented for the occasion, that I had accidentally fallen through the trap-door of the cellar, and had there lain stunned.鈥�. You can't have a bloody cellar if you only have two dimensions and you can鈥檛 鈥渇all through鈥� anything.
鈥� Another error (I think) is the existence of cupboards in Flatland. If there is no depth or verticality you can't have cupboards!
鈥� The 3D world is called Spaceland, it is not our world. Their most popular singer is probably Britney Sphere. (汀掳 蜏蕱 汀掳)
鈥� I initially thought this book was a collaboration between two abbots.
Quotes:
Yet even in our best regulated and most approximately Circular families I cannot say that the ideal of family life is so high as with you in Spaceland. There is peace, in so far as the absence of slaughter may be called by that name.
In a word, to comport oneself with perfect propriety in Polygonal society, one ought to be a Polygon oneself. Such at least is the painful teaching of my experience.
Doubtless, the life of an Irregular is hard; but the interests of the Greater Number require that it shall be hard. If a man with a triangular front and a polygonal back were allowed to exist and to propagate a still more Irregular posterity, what would become of the arts of life?
You, who are blessed with shade as well as light, you, who are gifted with two eyes, endowed with a knowledge of perspective, and charmed with the enjoyment of various colours, you, who can actually SEE an angle, and contemplate the complete circumference of a circle in the happy region of the Three Dimensions鈥攈ow shall I make clear to you the extreme difficulty which we in Flatland experience in recognizing one another's configuration?
Hipster Square
June 9, 2017
I give it an extra star for it's originality, it's uniqueness. The concept was genius, Abbott was probably a math genius himself. However, as a work of literature it does not hold up well. It has a shadowy similarity to , but falls well short of that Swift classic.
March 19, 2015
This was one crazy, opium fuelled, brilliant book about geometry and different dimensions and I am going to explain it the best way I can but Edwin A Abbott does it so much better.
Here is a story of Square who is a square and lives in a two dimensional world of geometrical figures. The first part of the book talks about the social breakdown of the Flatland and it is a thinly disguised satire on the Victorian society. People are divided into classes according to their geometry and the worst off are women who are not even figures; they are just straight lines. They have few rights and no one actually takes their intellect seriously. On the other hand they are dangerous because being straight lines they can easily pierce any figure. A woman from behind looks just like a dot, you might miss her until it鈥檚 to late and she has stabbed you. Different parts of Flatland developed different strategies for dealing with the danger, from not allowing women to leave their houses, to forcing them to constantly wiggle their bums, so they are visible from far. They should also sound a 鈥榩eace-cry鈥� when out and about, in case anyone missed the wiggling bum. Seriously children, don鈥檛 do drugs. It makes you write things like that.
The second part of the book gets more interesting as it delves deeper into the concept of dimensions. As I said, our hero lives in a two-dimension reality. Try to imagine such a world. You probably see it as a piece of paper with various figures drawn on it. Of course, that鈥檚 how a creature from 3D world would see it. You鈥檙e looking at it from above, i.e from the third dimension. If a 2D world was your entire reality you would only be able to see lines and dots. Your eyes would be on the same level as the figures and you would see everything in one dimension and infer the second dimension because you can move in it and you have learnt it through experience.
The same way we can鈥檛 actually see the third dimension but we can tell it鈥檚 there. We know we can move in three dimensions and we know about perspective, light, shadow, etc. It is easier for us to understand a two-dimension reality than it is to imagine a four-dimension one. We can see it perfectly when our Square visits a one dimensional land and he laughs at it and tries to explain to the King that there is more to life than just looking at a dot in front of you. There is another dimension where there are not only dots but lines as well. The King of course laughs him off. Yet, when Square is confronted by Sphere who tells him about the third dimension and shows him 鈥榯ricks鈥� that the third dimension allows him to do, Square is just as incredulous.
Even though the mathematics tells him there must be another dimension (and another, and another), he can鈥檛 quite believe it until Sphere shows him a little bit of a 3D world. Then he is a convert, and he quickly assumes there must be more dimensions. Fourth and fifth and ad infinitum. I think while reading this I got as close as I would ever get to understanding and imagining a 4D world. If in a 3D world we can see the insides of everything of a 2D world, then I suppose a in 4D world we would be able to actually SEE all three dimensions, all the insides of everything. My brains hurts. Am I making any sense? I thought I could see it but now it鈥檚 been a week after I finished reading the book and had those vivid dreams about the fourth dimension. The vision pales. I still believe in it but I can no longer grasp it. Just like the poor Square, back in his 2D-Land, thrown in prison for preaching revolution, still believes in the third dimension, but can no longer conjure the image of a Sphere in his head. Sometimes he feels he can almost see it again for half a second, and then it鈥檚 gone.
Here is a story of Square who is a square and lives in a two dimensional world of geometrical figures. The first part of the book talks about the social breakdown of the Flatland and it is a thinly disguised satire on the Victorian society. People are divided into classes according to their geometry and the worst off are women who are not even figures; they are just straight lines. They have few rights and no one actually takes their intellect seriously. On the other hand they are dangerous because being straight lines they can easily pierce any figure. A woman from behind looks just like a dot, you might miss her until it鈥檚 to late and she has stabbed you. Different parts of Flatland developed different strategies for dealing with the danger, from not allowing women to leave their houses, to forcing them to constantly wiggle their bums, so they are visible from far. They should also sound a 鈥榩eace-cry鈥� when out and about, in case anyone missed the wiggling bum. Seriously children, don鈥檛 do drugs. It makes you write things like that.
The second part of the book gets more interesting as it delves deeper into the concept of dimensions. As I said, our hero lives in a two-dimension reality. Try to imagine such a world. You probably see it as a piece of paper with various figures drawn on it. Of course, that鈥檚 how a creature from 3D world would see it. You鈥檙e looking at it from above, i.e from the third dimension. If a 2D world was your entire reality you would only be able to see lines and dots. Your eyes would be on the same level as the figures and you would see everything in one dimension and infer the second dimension because you can move in it and you have learnt it through experience.
The same way we can鈥檛 actually see the third dimension but we can tell it鈥檚 there. We know we can move in three dimensions and we know about perspective, light, shadow, etc. It is easier for us to understand a two-dimension reality than it is to imagine a four-dimension one. We can see it perfectly when our Square visits a one dimensional land and he laughs at it and tries to explain to the King that there is more to life than just looking at a dot in front of you. There is another dimension where there are not only dots but lines as well. The King of course laughs him off. Yet, when Square is confronted by Sphere who tells him about the third dimension and shows him 鈥榯ricks鈥� that the third dimension allows him to do, Square is just as incredulous.
Even though the mathematics tells him there must be another dimension (and another, and another), he can鈥檛 quite believe it until Sphere shows him a little bit of a 3D world. Then he is a convert, and he quickly assumes there must be more dimensions. Fourth and fifth and ad infinitum. I think while reading this I got as close as I would ever get to understanding and imagining a 4D world. If in a 3D world we can see the insides of everything of a 2D world, then I suppose a in 4D world we would be able to actually SEE all three dimensions, all the insides of everything. My brains hurts. Am I making any sense? I thought I could see it but now it鈥檚 been a week after I finished reading the book and had those vivid dreams about the fourth dimension. The vision pales. I still believe in it but I can no longer grasp it. Just like the poor Square, back in his 2D-Land, thrown in prison for preaching revolution, still believes in the third dimension, but can no longer conjure the image of a Sphere in his head. Sometimes he feels he can almost see it again for half a second, and then it鈥檚 gone.
October 6, 2016
Un racconto fantastico a pi霉 dimensioni con una velata (neanche poi troppo) critica alla chiusura mentale. Geniale.
November 20, 2024
5 per la seconda parte e 3 per la prima, che a tratti risulta un po鈥� noiosa essendo una sorta di elenco delle regole di Flatlandia.
In ogni caso, geniale!
In ogni caso, geniale!
September 7, 2024
Very strange
Review of free Kindle edition
ASIN: B0083ZRQR4
124 pages
I have long considered FLATLAND to be an overrated mostly boring book. However it is supposed to be a classic, admired and enjoyed by many people some of whom are considered to be or consider themselves to be intellectuals. So I thought, maybe it's me. Maybe a deficiency in my ability to grasp the fine qualities of the book prevents me from understanding how great it is. Or maybe my imagination is sub par. Then I read a passage about FLATLAND from THE POT THIEF WHO STUDIED EDWARD ABBEY by J. Michael Orenduff. Orenduff, a former college professor with his PhD in Mathematical Logic, a former university president and chancellor is now a full-time author known mainly for writing the Pot Thief Mystery Series. He should understand FLATLAND as a mathematician and as an author. Here is what his characters say about FLATLAND:
鈥淎ll work is 3-D,鈥� said Martin.
We stared at him.
He looked at me. 鈥淩emember that book Flatland you made me read?鈥�
鈥淚 didn鈥檛 make you read it.鈥�
鈥淲hen a white college student visits a fourteen-year-old dropout on the rez and suggests a book, that鈥檚 the same as making me read it.鈥�
鈥淏ut you liked it, right?鈥�
鈥淵eah, because it made me feel smarter than the guy who wrote it.鈥�
鈥淗ow so?鈥� asked Sharice.
鈥淗e says the men who live in Flatland are polygons. The fewer sides a man has, the lower he is on the social scale. So triangles are the lowest level, squares are higher, pentagons higher and so on. But he also says they can see each other and interact, which is impossible. Because if they were truly two-dimensional, they would have no sides, so there would be nothing to see.鈥�
鈥淵ou could see them from the top,鈥� said Susannah, 鈥渁nd from that vantage point, you could also see how many sides they have.鈥�
鈥淣o. To see them from on top, you鈥檇 have to be above them. But there is no up in Flatland. And there is no down. There is only north, south, east and west. So they wouldn鈥檛 even know other men existed.鈥�
鈥淭hey would when they bumped into them,鈥� she said.
He shook his head and placed two pennies on the table, sliding them until they touched. 鈥淭hese pennies can bump into each other because they have sides. But imagine them without sides. I don鈥檛 mean just really flat. I mean no side dimension at all. The men in Flatland can鈥檛 bump into each other because they have no sides.鈥�
鈥淲hy do you keep calling them men? Aren鈥檛 there women in Flatland?鈥�
鈥淪ure. The author says they are straight lines.
鈥漇he shook her head. 鈥淪heesh. I might have guessed. The women are the lowest life-forms because they have only one dimension.鈥�
鈥淩ight. And he makes the same sort of mistake in describing them, saying that seen from straight-on they look like a point. But you can鈥檛 see the end of a line because that would require that it have some height. Lines have only length. You could see them from below or above but not in a world that has only two dimensions.鈥�
鈥淗e says something else about women,鈥� I noted. 鈥淏ecause of their lack of intelligence, they accidentally pierce and kill people without even knowing it. But ten minutes later they can鈥檛 remember it happening.鈥�
Sharice stared at me. 鈥淎nd you made him read that?鈥�
鈥淔or the math part. I knew he was smart enough not to believe the stuff about women.鈥�
鈥淗e was also smart enough not to believe the stuff about math. A guy who thinks you can see something that doesn鈥檛 have sides 鈥ait, they can鈥檛 see anything anyway. If they had eyes, they would have to be on their surface, because they have no sides. So the only direction their eyes could look would be up. But there is no up.鈥�
鈥淪ee,鈥滻 said, trying to move beyond my having forced a misogynist book on Martin, 鈥淵ou鈥檙e also smarter than the author.鈥�
I agree with Mr. Orenduff and his fictional characters. That's my position and I'm sticking to it.
There are no illustrations in the free Kindle edition. However, Amazon offers the Distinguished Chiron Edition with illustrations by the author. This is supposed to be some kind of improvement of the original 1884 edition. The illustrations which I examined seem to confirm Mr. Orenduff's opinions by depicting a very flat three dimensional world instead of a two dimensional one.
Review of free Kindle edition
ASIN: B0083ZRQR4
124 pages
I have long considered FLATLAND to be an overrated mostly boring book. However it is supposed to be a classic, admired and enjoyed by many people some of whom are considered to be or consider themselves to be intellectuals. So I thought, maybe it's me. Maybe a deficiency in my ability to grasp the fine qualities of the book prevents me from understanding how great it is. Or maybe my imagination is sub par. Then I read a passage about FLATLAND from THE POT THIEF WHO STUDIED EDWARD ABBEY by J. Michael Orenduff. Orenduff, a former college professor with his PhD in Mathematical Logic, a former university president and chancellor is now a full-time author known mainly for writing the Pot Thief Mystery Series. He should understand FLATLAND as a mathematician and as an author. Here is what his characters say about FLATLAND:
鈥淎ll work is 3-D,鈥� said Martin.
We stared at him.
He looked at me. 鈥淩emember that book Flatland you made me read?鈥�
鈥淚 didn鈥檛 make you read it.鈥�
鈥淲hen a white college student visits a fourteen-year-old dropout on the rez and suggests a book, that鈥檚 the same as making me read it.鈥�
鈥淏ut you liked it, right?鈥�
鈥淵eah, because it made me feel smarter than the guy who wrote it.鈥�
鈥淗ow so?鈥� asked Sharice.
鈥淗e says the men who live in Flatland are polygons. The fewer sides a man has, the lower he is on the social scale. So triangles are the lowest level, squares are higher, pentagons higher and so on. But he also says they can see each other and interact, which is impossible. Because if they were truly two-dimensional, they would have no sides, so there would be nothing to see.鈥�
鈥淵ou could see them from the top,鈥� said Susannah, 鈥渁nd from that vantage point, you could also see how many sides they have.鈥�
鈥淣o. To see them from on top, you鈥檇 have to be above them. But there is no up in Flatland. And there is no down. There is only north, south, east and west. So they wouldn鈥檛 even know other men existed.鈥�
鈥淭hey would when they bumped into them,鈥� she said.
He shook his head and placed two pennies on the table, sliding them until they touched. 鈥淭hese pennies can bump into each other because they have sides. But imagine them without sides. I don鈥檛 mean just really flat. I mean no side dimension at all. The men in Flatland can鈥檛 bump into each other because they have no sides.鈥�
鈥淲hy do you keep calling them men? Aren鈥檛 there women in Flatland?鈥�
鈥淪ure. The author says they are straight lines.
鈥漇he shook her head. 鈥淪heesh. I might have guessed. The women are the lowest life-forms because they have only one dimension.鈥�
鈥淩ight. And he makes the same sort of mistake in describing them, saying that seen from straight-on they look like a point. But you can鈥檛 see the end of a line because that would require that it have some height. Lines have only length. You could see them from below or above but not in a world that has only two dimensions.鈥�
鈥淗e says something else about women,鈥� I noted. 鈥淏ecause of their lack of intelligence, they accidentally pierce and kill people without even knowing it. But ten minutes later they can鈥檛 remember it happening.鈥�
Sharice stared at me. 鈥淎nd you made him read that?鈥�
鈥淔or the math part. I knew he was smart enough not to believe the stuff about women.鈥�
鈥淗e was also smart enough not to believe the stuff about math. A guy who thinks you can see something that doesn鈥檛 have sides 鈥ait, they can鈥檛 see anything anyway. If they had eyes, they would have to be on their surface, because they have no sides. So the only direction their eyes could look would be up. But there is no up.鈥�
鈥淪ee,鈥滻 said, trying to move beyond my having forced a misogynist book on Martin, 鈥淵ou鈥檙e also smarter than the author.鈥�
I agree with Mr. Orenduff and his fictional characters. That's my position and I'm sticking to it.
There are no illustrations in the free Kindle edition. However, Amazon offers the Distinguished Chiron Edition with illustrations by the author. This is supposed to be some kind of improvement of the original 1884 edition. The illustrations which I examined seem to confirm Mr. Orenduff's opinions by depicting a very flat three dimensional world instead of a two dimensional one.
January 3, 2016
At the outset... the 5 stars are entirely subjective. I love maths, I love playing mathematical games, I love philosophising about maths. So this book is perfect for me. But if maths is not your cup of tea, you may not enjoy it as much as I did.
I first read about this book in one of Martin Gardner's "Mathematical Games" anthologies, and was enthralled by the concept. (In fact, he discusses two books: Flatland by Edwin A. Abbot and An Episode of Flatland by Charles Hinton written with the same premise. He says Hinton's book is better, and I have managed to locate an online version recently, but have not had time to read it so far.)
We live in a world of three dimensions. It is easy for us to deal with one dimension (the line), two dimensions (the plane) and three dimensions (space). But can we conceptualise a fourth dimension? It is well-nigh impossible, for our whole being is tied up on this three-dimensional paradigm.
Abbot's fictional world is two-dimensional. The characters move about on a flat landscape. They cannot imagine a third dimension. The narrator of the story, A. Square, is living the relatively comfortable life of a country gent until he is snatched up into "Spaceland" by a sphere, a three-dimensional being. He has a view of his land from a three-dimensional perspective, and Square is never the same again. He comes back to preach the concept of Space to his fellow countrymen and is promptly incarcerated in an asylum as a lunatic.
There is no story in this short novella: it is more of a mathematical exploration and social commentary. The first part uses the Flatland society to poke fun at Victorian norms, and is quite entertaining. The inhabitants of Flatland are all geometrical figures: social pedigree is conferred by the number of sides one has, the lowliest being the isoceles triangles (the soldiers) and the highest being the cirles (the priests). (The circle is a special instance of a polygon with an infinite number of sides.) The male children of a member of one class are usually born with one more side than the parent, so social climbing is possible. However, the women are all single lines: they can't aspire to be anything other than "women"! There are also irregular polygons, who are social misfits.
Abbot explains at length the geography and history of his society. The "Chromatic Revolution" where an attempt to overthrow the established order by a scheming "irregular" is scuttled by a clever circle, through an inspiring speech in parliament worthy of Mark Antony, is especially hilarious.
In the second part, the story submerges itself in the philosophy of maths. The protagonist has a vision of "Lineland", a world of a single dimension: he tries to explain Flatland to the King of that realm, but with little success. Then, our hero has a visit from a Sphere, an inhabitant of "Spaceland", and he faces the same problem in comprehending the third dimension as the king of Lineland had in comprehending the second (later, the Sphere demonstrates the same shortsight when Square moots the possibility of a fourth dimension).
Square is transported into Spaceland by Sphere, and suddenly he can see Flatland from the outside: including the inside of the houses and the intestines of the inhabitants, all at the same time! He also comprehends that the magical ability of a Spaceland denizen to move in and out of Flatland wherever he/ she wishes is nothing but a question of simple three-dimensional geometry. Square also is witness to a parliarmentary meeting where the Sphere makes a surprise appearance, to try to convince the rulers of Flatland about the existence of space, but to no avail. The preaching of space is a state crime in Flatland, with the penalty of either death or life in confinement(according to the social status of the individual)- the ultimate fate of the narrator of the story.
Yet even though he is destined to spend his remaining life in an asylum, Square is not willing to let go of his vision of Space. Once seen, he is transformed for life.
Abbot, a teacher and theologician, uses his knowledge of philosophy and mathematics not only to create a satire, but also to raise big questions about the limitations of perception in general. It is an extremely enjoyable read, and the issues it raises will stay with you even after you finish it.
Since it is available online free from Gutenberg, I suggest everyone to give it a try.
I first read about this book in one of Martin Gardner's "Mathematical Games" anthologies, and was enthralled by the concept. (In fact, he discusses two books: Flatland by Edwin A. Abbot and An Episode of Flatland by Charles Hinton written with the same premise. He says Hinton's book is better, and I have managed to locate an online version recently, but have not had time to read it so far.)
We live in a world of three dimensions. It is easy for us to deal with one dimension (the line), two dimensions (the plane) and three dimensions (space). But can we conceptualise a fourth dimension? It is well-nigh impossible, for our whole being is tied up on this three-dimensional paradigm.
Abbot's fictional world is two-dimensional. The characters move about on a flat landscape. They cannot imagine a third dimension. The narrator of the story, A. Square, is living the relatively comfortable life of a country gent until he is snatched up into "Spaceland" by a sphere, a three-dimensional being. He has a view of his land from a three-dimensional perspective, and Square is never the same again. He comes back to preach the concept of Space to his fellow countrymen and is promptly incarcerated in an asylum as a lunatic.
There is no story in this short novella: it is more of a mathematical exploration and social commentary. The first part uses the Flatland society to poke fun at Victorian norms, and is quite entertaining. The inhabitants of Flatland are all geometrical figures: social pedigree is conferred by the number of sides one has, the lowliest being the isoceles triangles (the soldiers) and the highest being the cirles (the priests). (The circle is a special instance of a polygon with an infinite number of sides.) The male children of a member of one class are usually born with one more side than the parent, so social climbing is possible. However, the women are all single lines: they can't aspire to be anything other than "women"! There are also irregular polygons, who are social misfits.
Abbot explains at length the geography and history of his society. The "Chromatic Revolution" where an attempt to overthrow the established order by a scheming "irregular" is scuttled by a clever circle, through an inspiring speech in parliament worthy of Mark Antony, is especially hilarious.
In the second part, the story submerges itself in the philosophy of maths. The protagonist has a vision of "Lineland", a world of a single dimension: he tries to explain Flatland to the King of that realm, but with little success. Then, our hero has a visit from a Sphere, an inhabitant of "Spaceland", and he faces the same problem in comprehending the third dimension as the king of Lineland had in comprehending the second (later, the Sphere demonstrates the same shortsight when Square moots the possibility of a fourth dimension).
Square is transported into Spaceland by Sphere, and suddenly he can see Flatland from the outside: including the inside of the houses and the intestines of the inhabitants, all at the same time! He also comprehends that the magical ability of a Spaceland denizen to move in and out of Flatland wherever he/ she wishes is nothing but a question of simple three-dimensional geometry. Square also is witness to a parliarmentary meeting where the Sphere makes a surprise appearance, to try to convince the rulers of Flatland about the existence of space, but to no avail. The preaching of space is a state crime in Flatland, with the penalty of either death or life in confinement(according to the social status of the individual)- the ultimate fate of the narrator of the story.
Yet even though he is destined to spend his remaining life in an asylum, Square is not willing to let go of his vision of Space. Once seen, he is transformed for life.
Abbot, a teacher and theologician, uses his knowledge of philosophy and mathematics not only to create a satire, but also to raise big questions about the limitations of perception in general. It is an extremely enjoyable read, and the issues it raises will stay with you even after you finish it.
Since it is available online free from Gutenberg, I suggest everyone to give it a try.
October 31, 2023
I call our world Flatland, not because we call it so, but to make its nature clearer to you, my happy readers, who are privileged to live in Space.
Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remaining fixed in their places, move freely about, on or in the surface, but without the power of rising above or sinking below it, very much like shadows-only hard with luminous edges-and you will then have a pretty correct notion of my country and countrymen.
In Flatland, everyone is a two-dimensional being. Each person鈥檚 place in the social order is determined by their number of sides and perfect angles (any physical deformity is usually met with death). At the top is the Priestly order of near-circular polygons. The Nobility starts with six-sided hexagons and above. Pentagons and squares鈥攐ur narrator is literally named 鈥淎. Square鈥濃€攆orm the Professional Class. After the middle class equilateral triangles, there are the soldiers and working-class isosceles triangles. Finally, at the very bottom of society, are all women, who are isosceles triangles of such a narrow angle that they are effectively straight lines, and forced to utter a 鈥減eace-cry鈥� at all times so they鈥檙e not invisible and stabby to the menfolk.
Flatland is really two books in one, and one is much better than the other. Let鈥檚 dispense with the bad first. The book was apparently intended and understood in its time as a satire of Victorian era society. Sure, and its strict hierarchy certainly has some parallels. But the rampant misogyny is utterly absurd. And this isn鈥檛 just a modern critique. When the author released a revised second edition鈥攊n 1884!鈥� he felt compelled to include a part apology/part defense for the harsh depiction of women in the story. So yeah, any value it has as a satire of Victorian era society is largely swamped by its sexist nonsense.
But as a geometrical thought experiment, Flatland is really cool. The story dives deeply into what a two-dimensional world would look like to its inhabitants. Then the second part of the story involves a visit to Flatland by a sphere from Spaceland, who tries to convince A. Square that there鈥檚 a three-dimensional world beyond Flatland. We see visions of one-dimensional Lineland, zero-dimensional Pointland, and consider the possibility of a four-dimensional land where instead of squares becoming cubes, cubes would become something grander, the never-named tesseract:
I鈥檓 glad I read this strange little story. The discussions about geometry in Flatland are highly imaginative. I鈥檇 recommend it to anyone capable of disregarding the grossly outdated societal notions.
November 8, 2018
3.5 stars.
This is a very personal rating. I think I would鈥檝e enjoyed this far more if I鈥檇 read it 10-20 years ago. The parts that were a pleasant surprise existed only to facilitate all the things I largely already knew.
This is by no means a bad book. On the one hand, this is a remarkable work of creativity by a man whose passion for his subject shines on every page. On the other, it may be better suited to capture the imagination of people in the early stages of their love for maths, geometry and higher dimensions. It simply came a little too late for me.
This is a very personal rating. I think I would鈥檝e enjoyed this far more if I鈥檇 read it 10-20 years ago. The parts that were a pleasant surprise existed only to facilitate all the things I largely already knew.
This is by no means a bad book. On the one hand, this is a remarkable work of creativity by a man whose passion for his subject shines on every page. On the other, it may be better suited to capture the imagination of people in the early stages of their love for maths, geometry and higher dimensions. It simply came a little too late for me.
December 18, 2021
I have to be honest...did not get as much from this book as I could have because of my decayed math skills (not that there was ever much there to decay). But it was a "bucket-list" book that I thought was quite inventive. Think this would be a really good STEM book for 8th graders; if they can understand the concepts here then I think they are ready for high school math.
February 19, 2021
For the most part I hate maths, other than stats & arithmetic, but I loved this absolutely mad book!
My copy didn't come with the line drawings, but they are available on I only found this site after I finished my read last night. I was happy with my imagination travelling with A Square trying to puzzle out his universe!
I wish I had discovered this book when I was at intermediate school. I was decent at maths until Year 10 and using my love of words may have made me try harder with maths - although I don't think anything could have made me & trig friends!
Knocked off a star for an often patronising attitude to women. Abbott may have thought he was being funny.
I didn't.
My copy didn't come with the line drawings, but they are available on I only found this site after I finished my read last night. I was happy with my imagination travelling with A Square trying to puzzle out his universe!
I wish I had discovered this book when I was at intermediate school. I was decent at maths until Year 10 and using my love of words may have made me try harder with maths - although I don't think anything could have made me & trig friends!
Knocked off a star for an often patronising attitude to women. Abbott may have thought he was being funny.
I didn't.
May 27, 2023
Un breve testo geniale e didattico, sorprendente pensando che 猫 stato redatto nel 1884 (e infatti era talmente avanti che all'epoca pass貌 sottotraccia, venendo poi ripreso qualche decennio dopo).
Il quadrato che vive in Flatlandia, mondo a due dimensioni, prima ci racconta il suo mondo e la sua vita, chi vi abita, come funzionano i rapporti sociali e quali leggi governano le loro vite. E qui si va di sottile satira e palate di fantasia.
Poi arriva l'elemento che cambia tutto, il visitatore dalla terza dimensione che poco a poco cambia la prospettiva del Quadrato aprendogli gli occhi all'universo in tre dimensioni.
E facendolo cos矛 bene da portarlo a ipotizzare ulteriori dimensioni, inizialmente rifiutate sdegnosamente dalla Sfera (riottosa a vedere la figura bidimensionale smettere di vederlo quale creatura suprema) e poi accettate e concesse, quasi con una vena di orgoglio per l'allievo.
Una lezione di matematica e geometria, l'ipotesi di dimensioni ulteriori per noi inconcepibili come l'altezza per le figure bidimensionali (o la lunghezza per quelle unidimensionali, o la pluralit脿 per quelle a zero dimensioni) e l'invito a rimanere con una mente aperta, a non cedere a facili dogmi, a cercare la verit脿.
Divertente e profetico.
Il quadrato che vive in Flatlandia, mondo a due dimensioni, prima ci racconta il suo mondo e la sua vita, chi vi abita, come funzionano i rapporti sociali e quali leggi governano le loro vite. E qui si va di sottile satira e palate di fantasia.
Poi arriva l'elemento che cambia tutto, il visitatore dalla terza dimensione che poco a poco cambia la prospettiva del Quadrato aprendogli gli occhi all'universo in tre dimensioni.
E facendolo cos矛 bene da portarlo a ipotizzare ulteriori dimensioni, inizialmente rifiutate sdegnosamente dalla Sfera (riottosa a vedere la figura bidimensionale smettere di vederlo quale creatura suprema) e poi accettate e concesse, quasi con una vena di orgoglio per l'allievo.
Una lezione di matematica e geometria, l'ipotesi di dimensioni ulteriori per noi inconcepibili come l'altezza per le figure bidimensionali (o la lunghezza per quelle unidimensionali, o la pluralit脿 per quelle a zero dimensioni) e l'invito a rimanere con una mente aperta, a non cedere a facili dogmi, a cercare la verit脿.
Divertente e profetico.
August 16, 2017
What a fantastic little thought-experiment, only really half-disguised as a story. Through his witty little parable, Abbott manages to explore the physical, mathematical, societal, philosophical and theological without once spoon-feeding his readers (OK, maybe there's a little bit of spoon-feeding in the earlier chapters).
It's only a shame, then, that this is without a doubt the most misogynist book I've ever read in my forty-odd years... Oh, well; I suppose nothing's perfect...
It's only a shame, then, that this is without a doubt the most misogynist book I've ever read in my forty-odd years... Oh, well; I suppose nothing's perfect...
August 19, 2018
Quite a charming allegory for the English society of the time, and boy does it show it's age. This is basically covered by everyone who reviewed this book, so I am not going to talk about that. What I noticed and I haven't seen anybody mention this yet, is the fact that at the time when this book was written Darwinian evolution has already grasped popular imagination. Just look how he talked about careful pairings between men and women to produce an equilateral triangle and then how each generation after that is achieved gets more sides until it reaches their version of perfection that is the circle. As I am aware people looked towards evolution with quite an optimism at the time and started envisioning utopias that will come to existence with careful work, selection and patience. Just look at the squares enlightenment at the prospect of 3 then 4 and as many dimensions it can possibly go.
Now this book, by it's writing style would get 3 stars, but no one can write something that after reading it makes me spend a night thinking about tesseracts (4 dimensional cubes) and glomes (4 dimensional spheres) and not be rewarded. Both mindfuckery and awesomeness.
Now this book, by it's writing style would get 3 stars, but no one can write something that after reading it makes me spend a night thinking about tesseracts (4 dimensional cubes) and glomes (4 dimensional spheres) and not be rewarded. Both mindfuckery and awesomeness.
March 7, 2020
This is without a doubt, the weirdest book I've ever read. Took me a little while to get into but once I did, I couldn't put the thing down. I would heartely recomend this to anyone not put off by the idea of shapes being the main characters.
February 3, 2023
Trama originale. Un po' lenta la prima parte, sin troppo veloce quella finale, ma non importa. Esclusione, pregiudizio, chiusura mentale e conseguente condanna di tutte e tre la fanno da padrone in questa storia godibile. Non sono in s茅 nuove le tematiche (basti pensare a Swift), ma il modo in cui sono trattate e la profondit脿 con la quale vengono sviscerate le ragioni che sostengono la necessit脿 di un fecondo relativismo culturale in luogo di una sterile dittatura assolutistica. Consigliato.
November 16, 2011
Questo libricino 猫 talmente matto e bello che dovete andare a comprarlo, e siccome so che le mie maniere dispotiche, e poco convincenti (purtroppo non ho le doti dei venditori di cose inutili che riescono a farti comprare di tutti convincendoti che siano utili)forse non vi indurranno all'acquisto, armatevi di convincitudine vostra, e andate a comprarvelo, o a rubarlo, o a prenderlo in prestito dalla biblioteca.
Perch茅? Leggete quanto segue
Se come me siete sempre stati delle perfette schiappe in matematica e geometria questo 猫 il libro che vi illuminer脿 di sapienza, una volta finito di leggerlo vorrete andare dai vostri vecchi professori/maestri, sbattere loro Flatlandia in testa e urlare MA CHE ACCIDENTI TI COSTAVA SPIEGARMELO COS矛 SEMPLICE?? . Purtroppo per貌 temo si tratti di un provvedimento anticostituzionale, dunque, anzich茅 prendervela con vecchi pedagoghi incapaci, potrete gentilmente ringraziare Abbott che nel 1882 ha scritto questo libro non so con quali intenti (devo ancora leggere saggi/articoli/, ma era troppo forte la voglia di parlarvene), ma di sicuro aveva capito che nel 1991 sarebbe nata una asina matematica come me, quindi ha voluto far parlare figure geometriche.
Se al contrario siete divini, comprendete la matematica e la geometria, avete l'occulto dono del far di conto e del comprendere combinazioni di lati, angoli, e quant'altro, tranquilli, a Flatlandia ce n'猫 anche per voi.
Per quanto siate saccenti, dubito infatti che in uno dei vostri compiti perfetti delle superiori o esami da 30/30 con lode dell'Universit脿, le figure geometriche abbiano mai preso a muoversi o a parlare.
Ma non 猫 tutto qui. Se pensavate che Geometria e Politica e Filosofia potessero difficilmente incastrarsi tra loro, vi sbagliavate. Perch茅 nella Geometria di Flatlandia la Politica sessista e razzista discrimina le Donne, gli Isosceli, gli Irregolari e assurge a razza perfetta i Circoli. Quando poi qualcuno vede o sente, anche per sua non colpa, qualcosa che non andava visto o sentito, viene fatto sparire. Che cosa assurda, si potrebbe pensare. E invece no. Succede anche da noi. Quindi tranquilli, a Flatlandia ci ritroverete molto.
Non incazzatevi troppo con Abbott se ce l'aveva con le donne.
Insomma, Dante ha reagito bene. Ma a volte gli approcci sessuali non vanno a finire in Commedie, sopratutto non in Divine.
La mia cartolina da Flatlandia smette qui di essere priva di raziocinio, scusate, ma sono ancora troppo esaltata.
Se decidete di farci un salto, tuttavia, chiedetemi l'indirizzo, perch茅 colleziono cartoline, e da Flatlandia le ricevo ben volentieri.
Perch茅? Leggete quanto segue
Se come me siete sempre stati delle perfette schiappe in matematica e geometria questo 猫 il libro che vi illuminer脿 di sapienza, una volta finito di leggerlo vorrete andare dai vostri vecchi professori/maestri, sbattere loro Flatlandia in testa e urlare MA CHE ACCIDENTI TI COSTAVA SPIEGARMELO COS矛 SEMPLICE?? . Purtroppo per貌 temo si tratti di un provvedimento anticostituzionale, dunque, anzich茅 prendervela con vecchi pedagoghi incapaci, potrete gentilmente ringraziare Abbott che nel 1882 ha scritto questo libro non so con quali intenti (devo ancora leggere saggi/articoli/, ma era troppo forte la voglia di parlarvene), ma di sicuro aveva capito che nel 1991 sarebbe nata una asina matematica come me, quindi ha voluto far parlare figure geometriche.
Se al contrario siete divini, comprendete la matematica e la geometria, avete l'occulto dono del far di conto e del comprendere combinazioni di lati, angoli, e quant'altro, tranquilli, a Flatlandia ce n'猫 anche per voi.
Per quanto siate saccenti, dubito infatti che in uno dei vostri compiti perfetti delle superiori o esami da 30/30 con lode dell'Universit脿, le figure geometriche abbiano mai preso a muoversi o a parlare.
Ma non 猫 tutto qui. Se pensavate che Geometria e Politica e Filosofia potessero difficilmente incastrarsi tra loro, vi sbagliavate. Perch茅 nella Geometria di Flatlandia la Politica sessista e razzista discrimina le Donne, gli Isosceli, gli Irregolari e assurge a razza perfetta i Circoli. Quando poi qualcuno vede o sente, anche per sua non colpa, qualcosa che non andava visto o sentito, viene fatto sparire. Che cosa assurda, si potrebbe pensare. E invece no. Succede anche da noi. Quindi tranquilli, a Flatlandia ci ritroverete molto.
Non incazzatevi troppo con Abbott se ce l'aveva con le donne.
Insomma, Dante ha reagito bene. Ma a volte gli approcci sessuali non vanno a finire in Commedie, sopratutto non in Divine.
La mia cartolina da Flatlandia smette qui di essere priva di raziocinio, scusate, ma sono ancora troppo esaltata.
Se decidete di farci un salto, tuttavia, chiedetemi l'indirizzo, perch茅 colleziono cartoline, e da Flatlandia le ricevo ben volentieri.
September 10, 2017
Videorecensione:
June 1, 2021
An incredible, timeless book.
Flatland should be prescribed reading for mathematics in secondary school, because it teaches so much conceptually using basic mathematics that everyone can understand. My interpretation below might clarify what I mean.
It demonstrates the utility of mathematics is abstraction, not measurement. It's what the units 'represent' that enables and motivates quantitative calculations. By counting something we bring a perception into existence, and we count when we care about and can demonstrate that it can be counted by more than one observer. Counting is also a subject decision insofar as we attribute a value to the variable counted, and a meaning to what its counting could mean. 'What counts has been counted'... in a nutshell?
It also demonstrates that mathematical models can model social systems. The strength of mathematical models of social systems is that they avoid any obvious sociocultural bias and so enables things that would normally be socially censored to be claimed as theoretical propositions. In short, it enables discourse about stereotypes and demonstrates the possibility of universal social or moral values. I feel a lot of the social norms of Flatland still apply today, in a way.
The importance of Spaceland I think is to demonstrate how it is nearly impossible to mathematically, or universally, demonstrate evidence of realities outside of measurable reality, because they begin and end in the subjective experience of the individual. Which is used as an argument both for and against religion. I think Flatland as a theological text favours spiritual belief in its lowly depiction of atheism or 'man as God' in Pointland as a less diverse system, geometrically speaking. I guess in a way it's calling existentialists navel-gazers insofar as they take their perception to solipsistic levels that is perhaps theologically speaking commits the blasphemy of 'self-as-a-God'. This shows why Flatland is so brilliant 鈥� it can simply, concisely and thoroughly show a complex understanding of human nature 鈥� such as how theists fail to explain their conviction, and atheists fail not to reject any conviction that conflicts with their original sense of perception. Most people don't get get that far in a debate in an hour let alone in less than 100 pages!
Ok... I think I've made my point. I think most people read this as some 'goofy maths' essay, but I see it as a social commentary that somehow covers the archetypes of society and the perception of reality in less than 100 pages and is somehow still ahead of its time a century later.
August 20, 2016
Unico, inclassificabile, geniale. Come dice Giorgio Manganelli nella postfazione "un capolavoro di illusionismo prospettico". Questa lettura 猫 stata uno stimolante esercizio mentale e di immaginazione, un invito al ragionamento come non ne apprezzavo da tanto, tanto tempo. Si sente che Abbott era un insegnante, perch猫 il linguaggio 猫 didattico e la struttura metodica. Tuttavia, per le sue implicazioni profonde, mi ha commossa e fatto venire la pelle d'oca. Consigliato a chiunque. Leggetelo, assaporatelo, regalatelo ai ragazzi. Questi sono libri speciali.
January 23, 2021
This may be allegory and/or satire, but I was hella bored. Chapter 1 is genius. The rest did nothing for me.
Concept > execution.
Concept > execution.
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